text:
Q: Speech Recognition don't works properly I'm programming a personal assistant with python on windows, it works so bad, some times I have the error 13 - permission denied to the file where the voice is stored. Another times it directly doesn't recognize my voice and other times it expend one minute or more for recognizing my voice. Looking at the code, what things I should improve to make it works better ?
import os
import time
import playsound
import speech_recognition as sr
from gtts import gTTS

def speak(text):
    tts = gTTS(text=text, lang="es-ES")
    filename = "voice.mp3"
    tts.save(filename)
    playsound.playsound(filename)

def get_audio():
    r = sr.Recognizer()
    with sr.Microphone() as source:
        audio = r.listen(source)
        said = ""

        try:
            said = r.recognize_google(audio, language="es-ES")
            print(said)
        except Exception as e:
            print("Exception: " + str(e))

    return said

speak("Di algo")
get_audio()

A: Welcome Samuel_05 I am also new around here!
To begin with instead of using a file to store aggregate data from gTTS, instead we can use a io.BytesIO (known as Bytes IO, Buffered IO, Virtual IO, and the list goes on...) object to store tts data pulled from Google in memory. Unfortunately, the playsound module used in your code doesn't support audio streaming via a file-like object. An alternative can be pygame it supports mp3 playback via a file-like object. Using a file-like object should solve your permission denied error.
Code
from pygame import mixer
import speech_recognition as sr
from gtts import gTTS
from io import BytesIO

# Adapted from:
# https://github.com/pndurette/gTTS/issues/26#issuecomment-607573170
def speak(text):
    with BytesIO() as f:
        tts = gTTS(text=text, lang="es-ES")
        tts.write_to_fp(f)  # Write speech to f
        f.seek(0)  # seek to zero after writing
        mixer.music.load(f)
        mixer.music.play()
        while mixer.music.get_busy():
            continue

def get_audio():
    r = sr.Recognizer()
    with sr.Microphone() as source:
        audio = r.listen(source)
        said = ""

        try:
            said = r.recognize_google(audio, language="es-ES")
            print(said)
        except Exception as e:
            print("Exception: " + str(e))

    return said

mixer.init()
speak("Di algo")


where's the closest one now? their online store locator couldn't find any close.
That's because they have already marked them as closed.
There are three around here, one at Anaheim Plaza, Tustin Marketplace, and Fountain Valley.
Fountain Valley was the first one opened in SoCal as I recall. Used to be an old Photon arena.
Yep, I remember going there a couple times when I was a kid.
Yah... basically they are starting with 10% off, which is nothing, and depending on sales... they'll go progressively higher and higher. One of the managers I talked to at the Tustin store said that they'll basically be open for a few more months.
I just wonder when MSFT is going to schedule me to go in and take back their interactive and their new display boxes for Vista and Office. Sigh.
Right now everything is at 5% to 10% off. Things like Zune players were 5%... and all software, video games, consoles, monitors, computers, laptops, and stuff were 10%. I'm sure it'll get much better in the coming weeks since they had originally gotten a BOATLOAD of copies of Vista and Office.
OH wait.. I said that already. Duh.


text:
require 'active_record'
require 'alive_state'

ActiveRecord::Base.establish_connection(adapter: 'sqlite3', database: ':memory:')

redpajama_set_name: RedPajamaGithub


Part of restoration works of a 1920's manufactory building. The unit covers a total surface of 166 m2 on two levels, plus 120 m2 of roof terrace.
The project starts from the preservation of the existing bearing structure, made of reinforced concrete pillars, beams and cast-on-site floorings with un-plastered ceiling surfaces.
Flooring is made of industrial birch wood, unsealed and wax finished.
Vertical partitions and false ceilings are made of gypsum board on aluminum structure. Other surfaces are made of extra clear glass laminated with white PVB film to allow a uniform light diffusion.
The stairway structures are made of steel and covered either with industrial wood parquet or else with "Wilton Nature" fitted carpet.
All sliding doors are made of white lacquered timbered wood. Curtains are made of black suede.
Cupboards and wall coverings are both made in black HPL with anodized aluminum finishing on two sides, and lacquered MDF. Kitchen compact volumes and top are in black Corian®, paneling and suspended elements are made of HPL.
Master bed in black lacquered MDF, guest bed in black HPL, both designed to measure. Wall hung console in mirror glass on MDF structure.
Tables and chairs, sofas and armchairs are all vintage pieces chosen from 60's/80's collections by famous designers.


text:
EUR-Lex Search results
Committee on Agriculture and Rural Development
Ordinary legislative procedure (COD)
Beef and veal
In title
In text
EU law and case-law (2)
Preparatory documents (2)
Please select at least one item to export
You must select an element!
Domain: All, Type of legislative procedure: Ordinary legislative procedure (COD), Date of document: 2014, Directory code, 3rd level: Beef and veal, Author: Committee on Agriculture and Rural Development, Search language: English
Save to My searches
Create in My alerts (RSS feeds)
Sort by Document titleDocument identifierDocument dateRelevance AscendingDescending
Customise shown information
Export selection Export all
P7_TA(2014)0262 Electronic identification of bovine animals ***I European Parliament legislative resolution of 2 April 2014 on the amended proposal for a regulation of the European Parliament and of the Council amending Regulation (EC) No 1760/2000 as regards electronic identification of bovine animals and deleting the provisions on voluntary beef labelling (COM(2012)0162 — C7-0114/2012 — 2011/0229(COD)) P7_TC1-COD(2011)0229 Position of the European Parliament adopted at first reading on 2 April 2014 with a view to the adoption of Regulation (EU) No …/2014 of the European Parliament and of the Council amending Regulation (EC) No 1760/2000 as regards electronic identification of bovine animals and labelling of beef
Select: 1
OJ C 408, 30.11.2017, p. 62–62 (BG, ES, CS, DA, DE, ET, EL, EN, FR, HR, IT, LV, LT, HU, MT, NL, PL, PT, RO, SK, SL, FI, SV)
OJ C 408, 30.11.2017, p. 62–62
CELEX number:
52014AP0262
BG, ES, CS, DA, DE, ET, EL, EN, FR, HR, IT, LV, LT, HU, MT, NL, PL, PT, RO, SK, SL, FI, SV
European Parliament, Committee on Agriculture and Rural Development, Committee on the Environment, Public Health and Food Safety
Date of document:
02/04/2014; Date of vote
 pdf
 html
P7_TA(2014)0263 Computer databases which are part of the surveillance networks in the Member States ***I European Parliament legislative resolution of 2 April 2014 on the proposal for a directive of the European Parliament and of the Council amending Council Directive 64/432/EEC as regards computer databases which are part of the surveillance networks in the Member States (COM(2011)0524 — C7-0229/2011 — 2011/0228(COD)) P7_TC1-COD(2011)0228 Position of the European Parliament adopted at first reading on 2 April 2014 with a view to the adoption of Directive 2014/…/EU of the European Parliament and of the Council amending Council Directive 64/432/EEC as regards computer databases which are part of the surveillance networks in the Member States

redpajama_set_name: RedPajamaCommonCrawl


text:
An unusual swelling in the neck
A A Abbasi1,
N S Harrop2
1SpR in Accident and Emergency Medicine, Blackpool Victoria Hospital, Blackpool, Lancashire, UK
2Consultant in Accident and Emergency Medicine, Blackpool Victoria Hospital, Blackpool, Lancashire, UK
Correspondence to:
A A Abbasi
Accident & Emergency Department, Blackpool Victoria Hospital, Blackpool, FY3 8NT; aaabbasi38hotmail.com
Venous thrombosis is a fundamental pathological entity. Our patient provides an opportunity to consider etiology in terms of Virchow's classic triad. We also draw attention to the effort syndrome, in which recurrent, vigorous exertion of an upper extremity is thought to produce venous thrombosis by virtue of local endothelial trauma.
Effort syndrome
upper limb DVT
A 44 year old man was referred by his General Practitioner to the A&E department with a 4 to 5 day history of left-sided neck swelling, symptoms of pleuritic chest pain, and weight loss of one stone.
He had just returned from holiday in Africa and had suffered from altitude sickness whilst climbing Mount Kilimanjaro. He had then suffered a prolonged bout of diarrhoea.
At a first visit, the GP had advised fluids because of dehydration. After a few days, the patient developed swelling in the left supraclavicular region with intermittent chest pain. He was, therefore, referred to A&E.
On examination he looked well. There was a non-pulsatile, diffuse swelling, in the left supraclavicular region. It extended to the base of the neck. Its margins were not palpable. The swelling was red, hot, and tender. There was no lymphadenopathy.
The chest was clear and the heart sounds were pure. Abdominal examination was unremarkable.
He was thought to have an abscess. However, chest x rays showed broadening of the left superior mediastinum with a small left basal effusion. Ultrasound of the neck demonstrated extensive thrombus in the left jugular, subclavian, and axillary veins (figure 1). A thoracic CT scan demonstrated diffuse tissue swelling in the left side of the neck and superior mediastinum. CT did not disclose any lymphadenopathy. There were bilateral pleural effusions, more so on the left (figure 2).
Showing an extensive thrombus within the left juglar vein, which extends to brachiocephalic and left axillary veins.
The patient was admitted to a medical ward and he was treated for venous thrombosis with low molecular weight heparin initially, then Warfarin. The swelling improved. His CRP, initially significantly elevated (200), returned to normal. His full blood count, renal functions and liver functions were normal
The patient was discharged after 5 days of hospital admission with advice to continue Warfarin for 6 months. He will have another CT scan after 6 weeks.
Spontaneous thrombosis of the axillary or subclavian veins was first postulated as a cause of upper extremity pain and swelling by Sir James Padget in 1875.1 Von Schroetter demonstrated thrombotic occlusion of upper limb veins, hence the Padget-Schroetter syndrome. More recently, the association between strenuous repetitive movement of the upper extremity and axillosubclavian thrombosis has been recognised and termed effort syndrome.2 Apart from iatrogenic factors such as catheter placement, venous thrombosis of the axillary, or subclavian vein may be caused by external compression by an anatomical structure such as a congenital cervical rib or by the pathological development of a local tumour.3
Virchow's triad explains thrombosis in terms of venous stasis, vessel wall abnormality or disorders of the blood itself.4
In this patient, it is suspected that venous stasis may have been added to local tissue trauma. The patient had worn a rucksack, possibly obstructing venous flow as well as causing trauma to the vessel wall. He had suffered altitude sickness and it is of interest that hypoxia may also produce endothelial injury.5 Finally, he had suffered a period of significant dehydration likely to have been attended by hemoconcentration and increased blood viscosity. In other patients, it is important to bear in mind that the occurrence of thrombosis at an unusual anatomic location may provide the first evidence of a hypercoagulable state, especially if there is a previous personal or a positive family history of thrombosis.6 Suitable investigations would then include a haemobilia screen.
Coon WW, Willis PW. Thrombosis of axillary and subclavian veins. Arch Surg1967;94:657–63.
Adams JT, DeWeese JA. Effort thrombosis of axillary and subclavian veins. Trauma1971;11:923–30.
Horattas MC, Wright DJ, Fenton AH. Changing concepts of deep vein thrombosis of the upper extremity-report of a series and review of the literature. Surgery1988;104:561–7.
Paget J. Clinical lectures and essays. Green London, UK: Longman, 1875.
Cromwell DL. Effort thrombosis of the subclavian and axillary veins: review of the literature. Ann Intern Medicine1960;52:1337–43.
Thomas DP, Roberts HR. Hypercoagulability in venous and arterial thrombosis. Ann Intern Med1997;126:638–44.


text:
require 'spec_helper'

RSpec.describe "Hello Gem", type: :feature do
  goal_feature "Account Management", "Manage Email Credentials", "Emails API" do

    pending "TODO: JSON suppport"

  end
end


Litigation is not something that UHY Crossleys would say that it specialises in, but in the past UHY Crossleys has proven to be adept and successful in the "Project Management" of litigation for clients in the UK and the Isle of Man. Such litigation has for instance involved disputes on the purchase and sale of companies and land, breaches of company law, equity (Trusts) and commercial contracts.
UHY Crossleys has also been involved in the taking of "proofs", discovery (general and specific), instructions to Tax and Legal Counsel (including Solicitors) and advising/suggesting a strategy profile for any litigation being undertaken. As part of this work, UHY Crossleys, on behalf of its clients, has instructed other professional firms to provide specific reports for the purposes of litigation and employed the services of investigative agents.


text:
\section{Introduction}

	%

	Let us consider the partial regularity of weak solutions for the three dimensional incompressible Navier-Stokes equations

	\begin{equation*} \label{NS} \tag{NS}
		\partial_t v - \Delta v + v \cdot \nabla v + \nabla \pi = 0,
		\quad \text{div}\, v = 0 \qquad \text{in } \Omega \times (0,T),
	\end{equation*}
	associated with the divergence-free initial data $v_0$, where $\Omega \subseteq \mathbb{R}^3$ and $T > 0$. The unknowns in \eqref{NS} are the velocity $v = (v_1,v_2,v_3) : \Omega \times (0,T) \to \mathbb{R}^3$ and the pressure $\pi : \Omega \times (0,T) \to \mathbb{R}$. It is well known that \eqref{NS} is invariant under the following natural scaling
	$$
		v(x,t) \mapsto v_\lambda(x,t) = \lambda v(\lambda x, \lambda^2 t) \quad \text{and} \quad \pi(x,t) \mapsto \pi_\lambda(x,t) = \lambda^2 \pi(\lambda x, \lambda^2 t) \quad \lambda > 0,
	$$
	which plays an important role in the regularity theory.

	The existence of global weak solutions $v \in L^\infty(0,T; L^2(\Omega)) \cap L^2(0,T; H^1(\Omega))$ of the initial boundary value problem to \eqref{NS} was provided a long time ago by Leray \cite{L1934} ($\Omega = \mathbb{R}^3$) and Hopf \cite{H1951} ($\Omega$ bounded) for finite energy initial data. These solutions  satisfy the global energy inequality and now are known as Leray-Hopf weak solutions. However, the uniqueness of global weak solutions and the existence of global strong solutions are still outsanding open problems.

	Various sufficient conditions have been provided to guarantee the regularity (and uniqueness) of weak solutions. One of the first and of the most well known of such conditions was indepently given by Prodi \cite{P1959}, Serrin \cite{S1962, S1963} and Ladyzhenskaya \cite{L1967} (also known as the (LPS) regularity condition, see also \cite{FJR1972}) which reads $v \in L^p(0,T;L^q(\mathbb{R}^3))$ where
	\begin{equation*} \tag{LPS} \label{LPS}
		\frac{2}{p} + \frac{3}{q} \leq 1 \qquad \text{for} \quad 3 \leq q \leq \infty.
	\end{equation*}
	The case $(p,q) = (\infty,3)$ has been investigated later by Escauriaza, Seregin and \v{S}ver\'{a}k \cite{ISS2003} (also for interior regularity cases).

	For a solution $v$ to \eqref{NS} we say that $z = (x,t) \in \mathbb{R}^3 \times (0,\infty)$ is a regular point of $v$ if there exists $r > 0$ such that $v \in L^\infty(Q_r(z))$. Otherwise, it will be called a singular point. The singular set of $v$ contains all singular points. The partial regularity theory for \eqref{NS} has been initiated by Scheffer \cite{S1976,S1977} and futher improved and simplified by Caffarelli, Kohn and Nirenberg \cite{CKN1982}, Lin \cite{L1998}, Ladyzhenskaya and Seregin \cite{LS1999} and Vasseur \cite{V2007}. They showed that the one-dimensional parabolic Hausdorff measure of the set of possible interior singular points for suitable weak solutions (see Definition \ref{def_sws}) is zero (also for one-dimensional Hausdorff measure). Note that if a weak solution satisfies \eqref{LPS} then it is suitable (see \cite{GKT2006}). Interior and near boundary regularity criteria for suitable weak solutions were also provided in terms of some norms with scaled factors by Gustafson, Kang and Tsai in \cite{GKT2006,GKT2007}.

	Regularity criteria based only on one velocity component started in \cite{NP1999} in which the authors provided the regularity in $D \times (t_1,t_2) \subset \Omega \times (0,T)$ if one velocity component $v_3$ is bounded in $D$. Then, Neustupa, Novotn\'{y} and Penel in \cite{NNP2002} proved the regularity under a (LPS)-type condition $v_3\in L^p(0,T;L^q(\mathbb{R}^3))$ with
	\begin{equation*}
		\frac{2}{p} + \frac{3}{q} \leq \frac{1}{2} \qquad \text{for} \quad 4 \leq p < \infty, \quad 6 < q \leq \infty,
	\end{equation*}
	This result was generalized by Kukavica and Ziane \cite{KZ2006} to
	\begin{equation*}
		\frac{2}{p} + \frac{3}{q} \leq \frac{5}{8} \qquad \text{for} \quad \frac{16}{5} \leq p < \infty, \quad \frac{24}{5} < q \leq \infty,
	\end{equation*}
	and by Cao and Titi \cite{CT2008} to
	\begin{equation*}
		\frac{2}{p} + \frac{3}{q} < \frac{2}{3} + \frac{2}{3q} \qquad \text{for} \quad 3 < p \leq \infty, \quad  \frac{7}{2} < q \leq \infty,
	\end{equation*}
	and also by Pokorn\'{y} and Zhou \cite{ZP2010} to
	\begin{equation*}
		\frac{2}{p} + \frac{3}{q} \leq \frac{3}{4} + \frac{1}{2q}  \qquad \text{for} \quad \frac{8}{3} \leq p < \infty, \quad \frac{10}{3} < q \leq \infty.
	\end{equation*}
	One of the first results on blow-up criteria via one velocity component in the scaling-invariant space $L^p(0,T;\dot{H}^{\frac{1}{2} + \frac{2}{p}}(\mathbb{R}^3))$\footnote{That means $\|v_\lambda\|_{L^p \big(0,\lambda^{-2}T;\dot{H}^{\frac{1}{2} + \frac{2}{p}}(\mathbb{R}^3) \big)} = \|v\|_{L^p \big(0,T;\dot{H}^{\frac{1}{2} + \frac{2}{p}}(\mathbb{R}^3) \big)}$ for $v_\lambda(x,t) = \lambda v(\lambda x,\lambda^2 t)$ with $\lambda > 0$.} was given by Chemin and Zhang in \cite{CZ2016} for $p \in (4,6)$, then by Chemin, Zhang and Zhang in \cite{CZZ2017} for $p \in (4,\infty)$ and recently extended to $p \in [2,\infty)$ in \cite{HLLZ2019} by Han, Lei, Li and Zhao. It is equivalent that if $v_3 \in L^p (0,T; \dot{H}^{\frac{1}{2} + \frac{2}{p}}(\mathbb{R}^3))$ then $v$ is regular in $\mathbb{R}^3 \times (0,T]$ for $p \in [2,\infty)$. Note that the embedding from the homogeneous Sobolev space $\dot{H}^{\frac{1}{2} + \frac{2}{p}}(\mathbb{R}^3)$ to $L^{\frac{3p}{p-2}}(\mathbb{R}^3)$ is continuous for $p > 2$ (see for example \cite{BCD2011}), and for $2 < p < \infty$, $\big(p,\frac{3p}{p-2}\big)$ satisfies \eqref{LPS}.

	Very recently, two significant results have been established. Firstly, Chae and Wolf \cite{CW2021} proved the regularity under strictly \eqref{LPS}, namely $\frac{2}{p} + \frac{3}{q} < 1$ for $3 < q \leq \infty$. Meanwhile, Wang, Wu and Zhang \cite{WWZ2020} obtained \eqref{LPS} in the sense of Lorentz spaces $v_3 \in L^{p,1}(0,T;L^q(\mathbb{R}^3))$ with $2 < p < \infty$ and $3 < q < \infty$, where $L^{p,1}$ denotes Lorentz spaces with respect to time variable (note that $L^{p,1} \subsetneq L^p$ for all $p > 1$). On the other hand, in \cite{BK2019} Bae and the first author proved regularity of Type I solution satisfying \eqref{LPS} condition for one component of the velocity.

	Further disscusions on this direction can be found in \cite{N2018}, where the author posed a question: \textit{Whether $v_3 \in L^p(0,T;L^q(\mathbb{R}^3)$ with $(p,q)$ satisfying \eqref{LPS} is sufficiently for the regularity of solution $v$ in $\mathbb{R}^3 \times (t_1,t_2)$?} In general, it is still an open problem at the time writing this paper.

	The aim of this paper is to provide local regularity criteria in terms of one velocity component both for local energy and suitable weak solutions. We provide initial regularity and local criteria in Theorems \ref{theo1}, \ref{theo2} and \ref{theo3}, respectively. As a consequence, we provide a partially (the $L^p_tL^q_x$-norm of $v_3$ is needed to be small enough) positive answer to the above question for $q \in [3,\infty]$. For $z = (x,t) \in \mathbb{R}^3 \times (0,\infty)$ and $r > 0$ we denote
	$$
		Q_r(z) := B_r(x) \times (t-r^2,t) \quad \text{and} \quad v_r(t) := \frac{1}{|B_r(x)|} \int_{B_r(x)} v(y,t) \,dy.
	$$
	 Before we state our main results, we recall a regularity criterion (see
	 \cite[Theorem 5.1]{W2015}), which is given as follows:
	There exists an absolute constant $\epsilon_W > 0$ such that if $(v,p)$ be a suitable weak solution in $Q_r(x_0,t_0)$ satisfying
	\begin{equation}\label{Wolf-2015}
		r^{-2}\|v\|^3_{L^3(Q_r(x_0,t_0))} \leq \epsilon_W
	\end{equation}
	for some $r \in (0,1)$ then $v \in L^\infty(Q_{\frac{r}{2}}(x_0,t_0))$.

	Now we are ready to state main theorems. Our first result reads as follows.

	\begin{theorem} \label{theo1}
		Let $(v,\pi)$ be a local energy solution \textnormal{(}resp., suitable weak solution\textnormal{)} to \eqref{NS} in $\mathbb{R}^3 \times (0,T)$ associated with the divergence-free initial data $v_0 \in L^2_{\textnormal{uloc}}(\mathbb{R}^3)$ \textnormal{(}resp., in the sense that  $\lim_{t \to 0} \|v(t)-v_0\|_{L^2(\mathbb{R}^3)} = 0$\textnormal{)}. Let $x_0 \in \mathbb{R}^3$, $M > 0$ and $\epsilon_0 \in (0,\epsilon_W]$, where $\epsilon_W$ is the constant in \eqref{Wolf-2015}. There exists $\delta_0(M,\epsilon_0) \in (0,1)$ with the following property. For some $0 < r_0 = r_0(M,\epsilon_0) \leq \sqrt{T}$ if
		\begin{equation} \label{v0}
			\sup_{r \in (0,r_0]} r^{-1}  \|v_0\|^2_{L^2(B_r(x_0))} \leq M
		\end{equation}
		and
		\begin{equation} \label{v3v0}
			\limsup_{r \to 0^+} r^{1-\frac{2}{p}-\frac{3}{q}} \|v_3\|_{L^p_tL^q_x(Q_r(x_0,r^2))} = 0 \qquad \text{for} \quad 1 \leq p,q \leq \infty
		\end{equation}
		hold, then
		\begin{equation*}
			(\delta_0 r_0)^{-2} \|v\|^3_{L^3(Q_{\delta_0 r_0}(x_0,(\delta_0 r_0)^2))}  \leq \epsilon_0.
		\end{equation*}
		In particular, $v$ is regular in $\{x_0\} \times (0,(\delta_1 r_0)^2]$ for some $\delta_1(M,\epsilon_0) \in (0,1)$.
	\end{theorem}

	For regularity criteria at a given point, an additional condition on the velocity is needed, in which the result is stated as follows.

	\begin{theorem} \label{theo2}
		Let $(v,\pi)$ be a local energy solution \textnormal{(}resp., suitable weak solution\textnormal{)} to \eqref{NS} in $\mathbb{R}^3 \times (0,\infty)$ associated with the divergence-free initial data $v_0 \in E^2$ \textnormal{(}resp., $v_0 \in L^2(\mathbb{R}^3)$\textnormal{)}. Let $z_0 = (x_0,t_0) \in \mathbb{R}^3 \times (0,\infty)$, $M > 0$ and $\epsilon_0 \in (0,\epsilon_W]$, where $\epsilon_W$ is the constant in \eqref{Wolf-2015}. There exists $\delta_0(M,\epsilon_0) \in (0,1)$ with the following property. For some $0 < r_0 = r_0(M,\epsilon_0,p_0,q_0) \leq \sqrt{t_0}$, assume that  one of following conditions holds
		\begin{align*}
			&(i) \sup_{r \in (0,r_0]} r^{1-\frac{2}{p_0}-\frac{3}{q_0}}  \|v-v_r\|_{L^{p_0}_tL^{q_0}_x(Q_r(z_0))} &\leq M \qquad \text{for} \quad  \frac{2}{p_0} + \frac{3}{q_0} \in [1,2), \frac{3}{2} < q_0 \leq \infty;
			\\
			&(ii) \sup_{r \in (0,r_0]} r^{2-\frac{2}{p_0}-\frac{3}{q_0}}  \|\nabla v\|_{L^{p_0}_tL^{q_0}_x(Q_r(z_0))} &\leq M \qquad \text{for} \quad  \frac{2}{p_0} + \frac{3}{q_0} \in [2,3), 1 < q_0 \leq \infty;
			\\
			&(iii) \sup_{r \in (0,r_0]} r^{2-\frac{2}{p_0}-\frac{3}{q_0}}  \|w\|_{L^{p_0}_tL^{q_0}_x(Q_r(z_0))} &\leq M \qquad \text{for} \quad  \frac{2}{p_0} + \frac{3}{q_0} \in [2,3), 1 < q_0 < \infty;
			\\
			&(iv) \sup_{r \in (0,r_0]} r^{3-\frac{2}{p_0}-\frac{3}{q_0}}  \|\nabla w\|_{L^{p_0}_tL^{q_0}_x(Q_r(z_0))} &\leq M \qquad \text{for} \quad  \frac{2}{p_0} + \frac{3}{q_0} \in [3,4), 1 \leq q_0 \leq \infty;
		\end{align*}
		where $w = \nabla \times  v$. In addition, suppose that
		\begin{equation} \label{v3z0}
			\limsup_{r \to 0^+} r^{1-\frac{2}{p}-\frac{3}{q}} \|v_3\|_{L^p_tL^q_x(Q_r(z_0))} = 0 \qquad \text{for} \quad 1 \leq p,q \leq \infty.
		\end{equation}
		Then
		\begin{equation} \label{W}
			(\delta_0 r_0)^{-2} \|v\|^3_{L^3(Q_{\delta_0 r_0}(z_0))} \leq \epsilon_0.
		\end{equation}
		In particular, $z_0$ is a regular point of $v$.
	\end{theorem}

	In particular, due to the structure of the local energy inequality we are able to consider a one-scaled condition as in \cite[Theorems 2.1]{KWM2017,KWM2019}, which is related to the pressure for suitable weak solutions but nor for local energy solutions. More precisely, the result is stated as follows.

	\begin{theorem} \label{theo3}
		Let $(v,\pi)$ be a local energy solution \textnormal{(}resp., suitable weak solution\textnormal{)} to \eqref{NS} in $\mathbb{R}^3 \times (0,\infty)$ associated with the divergence-free initial data $v_0 \in E^2$ \textnormal{(}resp., $v_0 \in L^2(\mathbb{R}^3)$\textnormal{)}. Let $z_0 = (x_0,t_0) \in \mathbb{R}^3 \times (0,\infty)$, $M > 0$ and $\epsilon_0 \in (0,\epsilon_W]$, where $\epsilon_W$ is the constant in \eqref{Wolf-2015}. There exist $\epsilon(M,\epsilon_0)$ and $\delta_0(M,\epsilon_0) \in (0,1)$ with the following property. For some $0 < r_0 = r_0(M,\epsilon_0,p,q) \leq \sqrt{t_0}$ if
		\begin{align*}
			\text{either} \quad r_0^{-2} \|v\|^3_{L^3(Q_{r_0}(z_0))}  &\leq M \qquad \text{for local energy solution}
			\\
			\text{or} \quad
			r_0^{-2} \left(\|v\|^3_{L^3(Q_{r_0}(z_0))} + \|\pi\|^\frac{3}{2}_{L^\frac{3}{2}(Q_{r_0}(z_0))} \right) &\leq M \qquad \text{for suitable weak solution}
		\end{align*}
		and
		\begin{equation} \label{v3r0}
			r^{1-\frac{2}{p}-\frac{3}{q}}_0 \|v_3\|_{L^p_tL^q_x(Q_{r_0}(z_0))} \leq \epsilon \qquad \text{for} \quad 1 \leq p,q \leq \infty
		\end{equation}
		hold then \eqref{W} follows and $z_0$ is a regular point of $v$.
	\end{theorem}

	\begin{remark} We add some comments on our results:
		\begin{enumerate}
			\item[1.] Theorem \ref{theo1} is inspired by \cite[Theorem 3.1]{KMT2021}, where the authors provided the initial regularity for $M$ sufficiently small in \eqref{v0}. As a consequence, the same conclusion holds if \eqref{v3v0} is replaced by $v_3 \in L^p_tL^q_x(Q_{r_0}(z_0))$ for $(p,q)$, $q>3$ satisfying \eqref{LPS}.

			\item[2.] Theorem \ref{theo2} extends the results in \cite[Theorem 1.1]{GKT2007} and \cite[Theorems 3.1 and 3.2]{WZ2014} in the sense that we only need one component is sufficiently small instead of the whole velocity or two components. A special case of our result shows that $v$ is regular if
			\begin{equation*}
				|v_1,v_2| \leq \frac{M}{\sqrt{T-t}} \quad \text{and} \quad |v_3| \leq \frac{\epsilon(M)}{\sqrt{T-t}},
			\end{equation*}
			which improves Leray's result \cite[page 227]{L1934}. In \cite[Theorem 1.3]{CW2021}, the authors proved that $z_0$ is a regular point under the following assumption for some $a \in (1,\infty)$ and for some $\rho > 0$
			\begin{equation} \label{CW}
				\limsup_{r \to 0^+} \, (-\log(r))^a r^{1-\frac{2}{p}-\frac{3}{q}} \|v_3\|_{L^p_tL^q_x(Q_{\rho,r}(z_0))} = 0,
			\end{equation}
			where $1 \leq \frac{2}{p} + \frac{3}{q} \leq \frac{3}{2}$, $3 \leq q < \infty$, $Q_{\rho,r}(z_0) = B'_{\rho}(x'_0) \times (x_{03}-r,x_{03}+r) \times (t_0-r^2,t_0)$ with $B'_{\rho}(x'_0) = \{y \in \mathbb{R}^2 : |y-x'_0| < \rho\}$ and $x_0 = (x_0',x_{03})$. It can be seen that \eqref{CW} is not given in a dimensionless form as \eqref{v3z0}, but we need one of the additional conditions on $v$. As a result, in Theorem \ref{theo2}, if one of (i),(ii),(iii) or (iv) holds for all $z_0$ and $v_3$ satisfies \eqref{LPS} with $q>3$ instead of \eqref{v3z0} then the global regularity follows.

			\item[3.] Theorem \ref{theo3} is inspired by \cite[Theorems 2.1]{KWM2017,KWM2019}, but we generalize the condition on $v_3$ to the scaled $L^p_tL^q_x$-norm instead of only on $L^3_{t,x}$-norm. We remark that the condition is not involved the pressure in the case of local energy solutions due to the decomposition \eqref{pressure_decomposition}. Moreover, Theorem \ref{theo3} also yields \cite[Theorem 2.2]{KWM2019}. More precisely, let $(v,\pi)$ be a Leray-Hopf weak solution to \eqref{NS} in $\mathbb{R}^3 \times (0,T)$. If $v$ is regular then for $q \geq 3$ and $t \in (0,T)$
			\begin{equation*}
				\|v_1(\cdot,t),v_2(\cdot,t)\|_{L^q(\mathbb{R}^3)} \leq \frac{M}{(T-t)^{\frac{1}{2}-\frac{3}{2q}}} \quad \text{and} \quad \|v_3(\cdot,t)\|_{L^q(\mathbb{R}^3)} \leq \frac{\epsilon(M)}{(T-t)^{\frac{1}{2}-\frac{3}{2q}}}.
			\end{equation*}

			\item[4.] In \cite[Theorem 1.1]{BK2019} the authors proved that smooth bounded solutions of \eqref{NS} in $\mathbb{R}^3 \times (-1,0)$ do not blow up at $t = 0$ if
			\begin{align*}
				&\|v(\cdot,t)\|_{L^\infty(\mathbb{R}^3)} \leq \frac{C}{\sqrt{-t}} \qquad \text{for } t \in (-1,0),
				\\
				&v_3 \in L^p(-1,0;L^q(\mathbb{R}^3))  \qquad \text{for} \quad  \frac{2}{p} + \frac{3}{q} = 1, q \in (3,\infty].
			\end{align*}
			They also provided the same result in the cases $v_3$ belongs to other invariant spaces such as weak Lebesgue, homogeneous Morrey–Campanato and homogeneous Besov spaces. Note that our conditions on $v_3$ as in \eqref{v3v0}, \eqref{v3z0} or \eqref{v3r0} can be considered in the above invariant spaces. We should mention that by using \eqref{CW} the authors in \cite{CW2021} provided the global regularity in the strict case, i.e.,
			\begin{equation*}
				v_3 \in L^p(0,T;L^q(\mathbb{R}^3))  \qquad \text{for} \quad \frac{2}{p} + \frac{3}{q} < 1, q \in (3,\infty],
			\end{equation*}
			which is due to the logarithmic factor. An immediate consequence of Theorem \ref{theo3} is that if for some $\epsilon(v,\pi) > 0$
			\begin{equation*}
				\|v_3\|_{L^p(0,\infty;L^q(\mathbb{R}^3))}  \leq \epsilon \qquad \text{for} \quad \frac{2}{p} + \frac{3}{q} \leq 1, q \in [3,\infty],
			\end{equation*}
			then $v$ is a regular solution in $\mathbb{R}^3 \times (0,\infty)$. Therefore, we leave an open question whether or not the above smallness assumption or the logarithmic factor in \eqref{CW} can be relaxed.

			\item[5.] Theorems \ref{theo1}-\ref{theo3} partially answer the question posed in \cite{N2018} and also hold for Leray-Hopf weak solutions under some futher assumption on $v_0$, for example in the case $v_0 \in L^2(\mathbb{R}^3) \cap L^3(\mathbb{R}^3)$. Note that for our results in the case of suitable weak solutions we can replace $\mathbb{R}^3$ by bounded domains $\Omega$ in which we need to require $0 < r_0 \leq \min\{\sqrt{t_0},\text{dist}(x_0,\partial \Omega)\}$.
		\end{enumerate}
	\end{remark}

	The rest of the paper is organized as follows: Section \ref{sec:pre} is devoted to recalling notions of weak solutions to \eqref{NS}. Proofs of Theorems \ref{theo1}-\ref{theo3} will be given in Sections \ref{sec:theo1}-\ref{sec:theo3}, respectively.

	%

	\section{Preliminaries} \label{sec:pre}

	%

	We introduce some notations and recall some notions of weak solutions to (\ref{NS}). For $x \in \mathbb{R}^3$, $r, t > 0$ and $z = (x,t)$  we denote $dz = dxdt$, $Q_r(z) = B_r(x) \times (t-r^2,t)$. Let $A$ be a set and $\delta \in \mathbb{R}$ we denote $\delta A = \{\delta a : a \in A\}$. For $A = (a_{ij})$ and $B = (b_{ij})$ be two matrices we define $A:B = \sum_{i,j} a_{ij} b_{ij}$ and $u \otimes v = (c_{ij})$ where $c_{ij} = u_i v_j$ for $u = (u_1, u_2, u_3), v = (v_1, v_2, v_3)$. For convenience, we denote $\partial_i = \partial_{x_i}$ for $1 \leq i \leq 3$. We use $C$ for denoting absolute constants. We also use the usual notions for Bochner, Lebesgue and Sobolev spaces. For $q \in [1,\infty]$, we define
	$$
	L^q_{\textnormal{uloc}}(\mathbb{R}^3) := \left\{f \in L^q_{\textnormal{loc}}(\mathbb{R}^3) : \|f\|_{L^q_{\textnormal{uloc}}(\mathbb{R}^3)} := \sup_{x_0 \in \mathbb{R}^3} \|f\|_{L^q (B_1(x_0))} < \infty \right\}.
	$$
	Let $E^q$ be the closure of $C^\infty_0(\mathbb{R}^3)$ in $L^q_{\textnormal{uloc}}(\mathbb{R}^3)$-norm. In \cite{LR2002}, the space $E^q$ can be defined by an equivalent way as follows
	$$
	E^q := \left\{f \in L^q_{\textnormal{uloc}}(\mathbb{R}^3) : \lim_{|x| \to \infty} \|f\|_{L^q(B_1(x))} = 0\right\}.
	$$
	We recall the well-known Gagliardo-Nirenberg interpolation inequality (see for example in \cite{CKN1982}) for $u \in H^1(B_r(x_0))$ with $r > 0$, $x_0 \in \mathbb{R}^3$
	\begin{equation} \label{Inter_i}
		\|u\|^{q}_{L^q(B_r(x_0))} \leq C \|\nabla u\|^{2a}_{L^2(B_r(x_0))} \|u\|^{q-2a}_{L^2(B_r(x_0))} + C r^{-2a} \|u\|^q_{L^2(B_r(x_0))},
	\end{equation}
	where $2 \leq q \leq 6$ and $a = \frac{3}{4}(q - 2)$. Let us recall the notions of suitable weak solutions (see \cite{CKN1982, L1998}) and local energy solutions or local Leray solutions (see \cite{BT2020, JS2013,JS2014,KMT2020_2,KMT2021, KS2007,LR2002}) to \eqref{NS}, respectively.

	\begin{definition}[Suitable weak solutions] \label{def_sws}
		For any domain $\Omega \subset \mathbb{R}^3$ and open interval $I \subset (0,\infty)$, we say $(v, \pi)$ is a suitable weak solution to \eqref{NS} in $\Omega \times I$ if it satisfies
		\begin{enumerate}
			\item $v \in L^\infty(I;L^2(\Omega)) \cap L^2(I;\dot{H}^1(\Omega))$, $\pi \in L^{\frac{3}{2}}(\Omega \times I)$;

			\item \eqref{NS} in the sense of distributions in $\Omega \times I$;

			\item and the local energy inequality
			\begin{align} \label{lei}
				\int_\Omega |v|^2 \varphi \,dx + 2  \int_{\Omega_s} |\nabla v|^2 \varphi \,dz
				&\leq \int_{\Omega_s} |v|^2 (\partial_t \varphi
				+ \Delta \varphi) +
				(|v|^2 + 2\pi) (v \cdot \nabla \varphi) \,dz
			\end{align}
			for $s \in I$, $\Omega_s = \Omega \times (0,s)$ and all non-negative $\varphi \in C^\infty_0(\Omega \times I)$.
		\end{enumerate}
	\end{definition}

	\begin{definition}[Local energy solutions] \label{def_les}
		A vector field $v \in L^2_{\textnormal{loc}}(\mathbb{R}^3 \times [0, T))$ is a local energy solution to \eqref{NS} with divergence free initial data $v_0 \in L^2_{\textnormal{uloc}}(\mathbb{R}^3)$ if
		\begin{enumerate}
			\item for some $\pi \in L^{\frac{3}{2}}_{\textnormal{loc}} (\mathbb{R}^3 \times [0, T))$, the pair $(v, \pi)$ is a distributional solution to \eqref{NS};

			\item for any $r > 0$,
			\begin{equation*}
				\esssup_{0 \leq t < \min\{r^2, T\}} \sup_{x_0 \in \mathbb{R}^3} \int_{B_r(x_0)} |v|^2 \,dx + \sup_{x_0 \in \mathbb{R}^3} \int^{\min\{r^2,T\}}_0 \int_{B_r(x_0)}|\nabla v|^2 \,dz < \infty,
			\end{equation*}
			\item for all compact subsets $K$ of $\mathbb{R}^3$ we have $v(t) \to v_0$ in $L^2(K)$ as $t \to 0^+$;

			\item $(v, p)$ satisfies the local energy inequality \eqref{lei} for all non-negative functions $\varphi \in C^\infty_0(Q)$ with all cylinder $Q$ compactly supported in $\mathbb{R}^3 \times (0, T)$;

			\item for every $x_0 \in \mathbb{R}^3$ and $r > 0$, there exists $c_{r, x_0} \in L^\frac{3}{2}((0, T))$ such that
			\begin{align} \label{pressure_decomposition}
				\pi(x, t) - c_{r,x_0}(t) &= \frac{1}{3}|v(x, t)|^2 + \textnormal{p.v.}  \int_{B_{3r}(x_0)} K(x - y) : (v \otimes v)(y, t) \,dy
				\nonumber\\
				&\quad + \int_{\mathbb{R}^3 \setminus B_{3r}(x_0)} (K(x - y) - K(x_0 - y)) : (v \otimes v)(y, t) \,dy
			\end{align}
			in $L^\frac{3}{2}(B_{2r}(x_0) \times (0, T))$ where $K(x) := \nabla^2\big(\frac{1}{4\pi|x|}\big)$;

			\item and for any compactly supported functions $w \in L^2(\mathbb{R}^3)$,
			\begin{equation*}
				\text{the function}\quad t  \mapsto \int_{\mathbb{R}^3} v(x, t) \cdot w(x) \,dx \quad \text{is continuous on } [0, T).
			\end{equation*}
		\end{enumerate}
	\end{definition}
	If $(v,p$) is a local energy solution to \eqref{NS} in $\mathbb{R}^3 \times (0,T)$ for all $T \in (0,\infty)$ then we say that it is a local energy solution in $ \mathbb{R}^3 \times (0, \infty)$. We recall a version of  Gronwall inequality due to Bradshaw and Tsai.

	\begin{lemma}[Lemma 2.2 in \cite{BT2020}] \label{lem_BT}
		Let $f \in L^\infty_{\textnormal{loc}}([0, T_0]; [0, \infty))$ satisfies
		$$
		f(t) \leq a + b \int^t_0 f(s) + f^m(s) \,ds \qquad \text{for } t \in [0, T_0]
		$$
		and for some constants $a,b > 0$, $m \geq 1$. Then
		$$
		f(t) \leq 2a \quad \forall t \in [0, T] \quad \text{where} \quad  T = \min\left\{T_0, \frac{C}{b(1 + a^{m-1})} \right\}.
		$$
	\end{lemma}

	%

	\section{Proof of Theorem \ref{theo1}} \label{sec:theo1}

	%

	\begin{proof}[Proof of Theorem \ref{theo1}]\quad $\bullet$\,\textnormal{(}The case of local energy solution\textnormal{)}\, Let $\gamma \in (0, \frac{r_0}{3}]$. The local energy inequality (see \cite[Theorem 3.4]{KMT2021}) with $\gamma \leq r \leq \frac{r_0}{3}$
	and $s \in (0,r^2_0]$ yields
	\begin{align*}
		E_r(s) &:= \esssup_{t \in (0,s)} \frac{1}{r} \int_{B_r(x_0)} |v(t)|^2 \,dx + \frac{1}{r} \int_0^s \int_{B_r(x_0)} |\nabla v|^2 \,dz + \frac{1}{r^2} \int_0^s \int_{B_r(x_0)} |\pi_{r_0,x_0}|^\frac{3}{2} \,dz
		\\
		&\leq 2M + \frac{C}{\gamma^2} \int_0^s \mathcal{E}_\gamma(t) \,dt + \frac{C}{r^2} \int_0^s \int_{B_{2r}(x_0)} |v|^3 \,dz + \frac{C}{r^2} \int_0^s \int_{B_{2r}(x_0)} |\pi_{r_0,x_0}|^\frac{3}{2} \,dz,
	\end{align*}
	where we used \eqref{v0} and \eqref{pressure_decomposition} with $(x,t) \in B_{2r_0}(x_0) \times (0,T)$
	\begin{align*}
		\pi_{r_0,x_0} &:= \pi(x,t) - c_{r_0,x_0}(t) = \frac{1}{3} |v(x,t)|^2 + p_1(x,t) + p_2(x,t),
		\\
		p_1(x,t) &:= \textnormal{p.v.} \int_{B_{3r_0}(x_0)} K(x - y) : (v \otimes v)(y, t) \,dy,
		\\
		p_2(x,t) &:= \int_{\mathbb{R}^3 \setminus B_{3r_0}(x_0)} (K(x - y) - K(x_0-y) : (v \otimes v)(y, t) \,dy,
		\\
		\mathcal{E}_\gamma(s) &:= \sup_{r \in [\gamma,r_0]} E_r(s).
	\end{align*}
	The cubic term is denoted by $R_3$ and can be estimated by using \eqref{Inter_i} and Young inequality as follows
	\begin{equation*}
		R_3 \leq \epsilon \mathcal{E}_\gamma(s) + \frac{C_\epsilon}{\gamma^2} \int^{s}_{0} \mathcal{E}^\frac{3}{2}_\gamma(t) + \mathcal{E}^3_\gamma(t) \,dt
	\end{equation*}
	for some absolute constant $\epsilon \in (0,1)$ to be specified later. For the pressure term which is denoted by $R_4$ and is bounded by using the Calder\'{o}n-Zygmund estimate
	\begin{align*}
		R_4 &\leq \frac{C}{r^2} \int_0^{s} \int_{B_{3r}(x_0)}  |v|^3 \,dz + \frac{C}{r^2} \int_0^{s}\int_{B_{2r}(x_0)} |p_2|^\frac{3}{2} \,dz.
	\end{align*}
	For any $x \in B_{2r}(x_0) \subset B_{2r_0}(x_0)$ and $y \in \mathbb{R}^3 \setminus B_{3r_0}(x_0)$ we have the fact that
	\begin{equation*}
		|K(x-y) - K(x_0-y)| \leq C\frac{|x-x_0|}{|x_0-y|^4} \leq \frac{Cr}{|x_0 - y|^4}.
	\end{equation*}
	Therefore, it follows that for $(x,t) \in B_{2r}(x_0) \times (0,s)$ with $s \in (0,r_0^2]$
	\begin{align*}
		|p_2(x,t)| &\leq Cr \int_{\mathbb{R}^3 \setminus B_{3r_0}(x_0)} \frac{|v(y,t)|^2}{|x_0-y|^4} \,dy
		\\
		&\leq C \sum^\infty_{i=0} \int_{B_{2^{i+1}r_0}(x_0) \setminus B_{2^ir_0}(x_0)} \frac{|v(y,t)|^2}{|x_0-y|^4} \,dy
		\\
		&\leq C \sum^\infty_{i=0} \frac{1}{2^{4i}}\int_{B_{2^{i+1}r_0}(x_0)} |v(y,t)|^2 \,dy
		\\
		&\leq C \esssup_{t\in (0,r_0^2)} \sup_{x_0 \in \mathbb{R}^3} \int_{B_{r_0}(x_0)} |v(x,t)|^2 \,dx =: V < \infty,
	\end{align*}
	which yields
	\begin{equation*}
		R_4 \leq CV^\frac{3}{2} + \epsilon \mathcal{E}_\gamma(s) + \frac{C_\epsilon}{\gamma^2} \int^{s}_{0} \mathcal{E}^\frac{3}{2}_\gamma(t) + \mathcal{E}^3_\gamma(t) \,dt
	\end{equation*}
	and for $0 < \gamma < r \leq \frac{r_0}{3}$
	\begin{equation*}
		E_r(s) \leq 2M + CV^\frac{3}{2} + 2\epsilon \mathcal{E}_\gamma(s) + \frac{C_\epsilon}{\gamma^2} \int^{s}_{0} \mathcal{E}_\gamma(t) + \mathcal{E}^3_\gamma(t) \,dt.
	\end{equation*}
	On the other hand, for $\frac{r_0}{3} < r \leq r_0$
	\begin{equation*}
		E_r(s) \leq \frac{9}{r_0} \left(\esssup_{t \in (0,r^2_0)} \int_{B_{r_0}(x_0)} |v(t)|^2 \,dx +  \int_{Q_{r_0}(x_0,r^2_0)} |\nabla v|^2 +  \frac{1}{r_0} |\pi_{r_0,x_0}|^\frac{3}{2} \,dz\right) := E_0 < \infty.
	\end{equation*}
	Therefore, by choosing $\epsilon = \frac{1}{4}$ we obtain for all $s \in (0,r^2_0]$ and for all $\gamma \in (0,r_0]$
	\begin{equation*}
		\mathcal{E}_\gamma(s) \leq C(E_0 + M + V^\frac{3}{2}) + \frac{C}{\gamma^2} \int^{s}_{0} \mathcal{E}_\gamma(t) + \mathcal{E}^3_\gamma(t) \,dt.
	\end{equation*}
	Applying Lemma \ref{lem_BT} to the above form one has
	\begin{equation*}
		\mathcal{E}_\gamma(s) \leq E_1, \qquad \forall s \in (0, \lambda \gamma^2], \forall \gamma \in (0,r_0],
	\end{equation*}
	where $E_1 := C(E_0 + M +  V^\frac{3}{2})$ and $\lambda := \frac{C}{1 + E_1^2} \leq 1$. It yields $E_r(r^2) \leq \lambda^{-1}E_1$ for all $r \in (0,\lambda r_0]$. In particular,
	\begin{equation*}
		E_r(r^2) \leq \lambda^{-1}(E_1 + E_0) +  =: E_2, \qquad \forall r \in (0,r_0].
	\end{equation*}
	We assume that the conclusion is not true, i.e.,
	\begin{equation*}
		(\delta_0 r_0)^{-2} \|v\|^3_{L^3(Q_{\delta_0 r_0}(x_0,(\delta_0 r_0)^2))} > \epsilon_0, \qquad \forall \delta_0 \in (0,1).
	\end{equation*}
	For $(x,t) \in Q_1(0,0)$ and $\delta \in (0,r_0]$ we define
	\begin{equation*}
		v_\delta(x,t) := \delta v(\delta x + x_0,\delta^2 t + \delta^2)
		\quad
		\text{and}
		\quad
		\pi_\delta(x,t) := \delta^2 \pi_{r_0,x_0}(\delta x + x_0,\delta^2 t + \delta^2).
	\end{equation*}
	Then $(v_\delta,\pi_\delta)$ is a sequence of suitable weak solutions to \eqref{NS} in $Q_1(0,0)$ since $(v,\pi_{r_0,x_0})$ is a suitable weak solution to \eqref{NS} in $Q_\delta(x_0,\delta^2)$ for all $\delta \in (0,r_0]$. Moreover, it can be seen from the bound of $(v,\pi)$ that
	\begin{equation*}
		\|v_\delta\|^2_{L^\infty(-1,0;L^2(B_1(0)))} + \|\nabla v_\delta\|^2_{L^2(-1,0;L^2(B_1(0)))} + 	\|\pi_\delta\|^\frac{3}{2}_{L^\frac{3}{2}(-1,0;L^\frac{3}{2}(B_1(0)))} \leq E_2.
	\end{equation*}
	It implies that there exist a subsequence of $(v_\delta,\pi_\delta)$ (still denoted by $(v_\delta,\pi_\delta$)) and a pair $(\bar{v},\bar{\pi})$ and by using Aubin-Lion lemma and interpolation we find that as $\delta \to 0$
	\begin{equation*}
		\left\{
		\begin{aligned}
			v_\delta  &\overset{\ast}{\rightharpoonup} \bar{v} \qquad \text{ in } L^\infty(-1,0;L^2(B_1(0))),
			\\
			\nabla v_\delta  &\overset{}{\rightharpoonup} \nabla \bar{v} \quad\, \text{ in } L^2(-1,0;L^2(B_1(0))),
			\\
			\pi_\delta  &\overset{}{\rightharpoonup} \bar{\pi} \qquad \text{ in } L^\frac{3}{2}(-1,0;L^\frac{3}{2}(B_1(0))),
			\\
			v_\delta &\to \bar{v} \qquad \text{ in } L^a(-1,0;L^a(B_1(0))) \qquad \text{for} \quad 1 \leq a < \frac{10}{3}.
		\end{aligned}
		\right.
	\end{equation*}
	It can be seen that $(\bar{v},\bar{\pi})$ is also a suitable weak solution to \eqref{NS} in $Q_1(0,0)$. In addition, using \eqref{v3v0} we obtain for $1 \leq p,q \leq \infty$
	\begin{equation*} \label{lim_v_delta}
		\limsup_{\delta \to 0^+} \|v_{\delta,3}\|_{L^p(-1,0;L^q(B_1(0)))} = \limsup_{\delta \to 0^+} \delta^{1-\frac{2}{p}-\frac{3}{q}} \|v_3\|_{L^p(0,\delta^2;L^q(B_\delta(x_0)))} = 0,
	\end{equation*}
	which implies that $\bar{v}_3 \equiv 0$. Thus, $(\bar{v},\bar{\pi})$ is also a suitable weak solution to "the limiting system" which is formally reduced from \eqref{NS} by setting $\bar{v}_3 = 0$. The authors in \cite[Theorem 3.1]{KWM2017} proved that $\bar{v}$ is regular. However, for some $0 < \nu < r_0^{-1}$ so that $0 < \delta \nu < 1$ we have
	\begin{equation*}
		(\nu r_0)^{-2} \|v_\delta\|^3_{L^3(Q_{\nu r_0}(0,0))}  = (\delta\nu r_0)^{-2} \|v\|^3_{L^3(Q_{\delta\nu r_0}(x_0,(\delta \nu r_0)^2))} > \epsilon_0,
	\end{equation*}
	and
	\begin{equation*}
		(\nu r_0)^{-2} \|\bar{v}\|^3_{L^3(Q_{\nu r_0}(0,0))}  \geq  \epsilon_0 \quad \text{as} \quad \delta \to 0,
	\end{equation*}
	which is a contradiction with the regularity of $\bar{v}$ by choosing $\nu$ sufficiently small. Therefore, the proof is complete by iteration and using the one scale regularity criterion given by \eqref{Wolf-2015}.

	$\bullet$\,\textnormal{(}The case of suitable weak solution\textnormal{)} In this case the proof is quite similar to that of for local energy solutions and we only need to estimate the pressure term with $\pi$ instaed of $\pi_{r_0,x_0}$. As in \cite[Theorem 3.1]{KMT2021}, we decompose the pressure as $\pi = p_1 + p_2$ with
	\begin{equation*}
		p_1(x,t) := - \frac{1}{3} \xi(x)|v(x,t)|^2 + \textnormal{p.v.} \int_{\mathbb{R}^3} K(x-y):(v \otimes v)(y,t) \xi(y) \,dy,
	\end{equation*}
	where $K$ is given as in \eqref{pressure_decomposition}, $\xi = \xi_{x_0}$ is a smooth cut-off function with $\xi = 1$ in $B_\rho(x_0)$ and supported in $B_{2\rho}(x_0)$ for some $\rho \in [3r,\frac{r_0}{2}]$, here $0 < \gamma \leq r \leq \frac{r_0}{8C_1}$ for some absolute constant $C_1$ will be given below and $\rho$ will be specified later. Since $p_2$ is harmonic in $B_{\rho}(x_0)$ and using the Calder\'{o}n-Zygmund estimate we find that
	\begin{align*}
		\int_{B_{2r}(x_0)} |\pi|^\frac{3}{2} \,dx
		&\leq C\int_{B_{2r}(x_0)} |p_1|^\frac{3}{2} \,dx + C\left(\frac{r}{\rho}\right)^3 \int_{B_\rho(x_0)} |p_2|^\frac{3}{2} \,dx
		\\
		&\leq C\int_{B_{2r}(x_0)} |p_1|^\frac{3}{2} \,dx + C\left(\frac{r}{\rho}\right)^3 \int_{B_\rho(x_0)} |p_1|^\frac{3}{2} \,dx  + C\left(\frac{r}{\rho}\right)^3 \int_{B_\rho(x_0)} |\pi|^\frac{3}{2} \,dx
		\\
		&\leq C\int_{B_{2\rho}(x_0)} |v|^3 \,dx + C\left(\frac{r}{\rho}\right)^3 \int_{B_\rho(x_0)} |\pi|^\frac{3}{2} \,dx,
	\end{align*}
	which implies for some absolute constant $C_1 > 1$
	\begin{align*}
		R_4 := \frac{C}{r^2} \int^s_0 \int_{B_{2r}(x_0)} |\pi|^\frac{3}{2} \,dz &\leq \frac{C}{r^2} \int^s_0\int_{B_{2\rho}(x_0)} |v|^3 \,dz + \frac{C_1r}{\rho} \frac{1}{\rho^2} \int^s_0 \int_{B_\rho(x_0)} |\pi|^\frac{3}{2} \,dz
		\\
		&\leq \frac{C}{r^2} \int^s_0\int_{B_{8C_1r}(x_0)} |v|^3 \,dz + \frac{1}{4} \mathcal{E}_\gamma(s)
		\\
		&\leq \frac{1}{4} \mathcal{E}_\gamma(s) + \epsilon \mathcal{E}_\gamma(s) + \frac{C_\epsilon}{\gamma^2} \int^{s}_{0} \mathcal{E}^\frac{3}{2}_\gamma(t) + \mathcal{E}^3_\gamma(t) \,dt
	\end{align*}
	by choosing $\rho = 4C_1r \in [3r,\frac{r_0}{2}]$ and using the estimate of $R_3$ with the fact that $8C_1r \in [\gamma,r_0]$. Thus the rest of the proof is almost the same that of the previous case. We omit the details and end the proof.
	\end{proof}

	%

	\section{Proof of Theorem \ref{theo2}} \label{sec:theo2}

	%

	\begin{proof}[Proof of Theorem \ref{theo2}]
\quad $\bullet$\,\textnormal{(}The case of local energy solution\textnormal{)}\,

	The local energy inequality gives us for $0 < r \leq \frac{r_0}{3}$
	\begin{align*}
		E(r) &:= \esssup_{t \in (t_0-r^2,t_0)} \frac{1}{r} \int_{B_r(x_0)} |v(t)|^2 \,dx + \frac{1}{r} \int_{Q_r(z_0)} |\nabla v|^2 \,dz + \frac{1}{r^2} \int_{Q_r(z_0)} |\pi_{r_0,x_0}|^\frac{3}{2} \,dz
		\\
		&\leq C\left(1 +  \frac{1}{9r^2} \|v\|^3_{L^3(Q_{3r}(z_0))}  + \max\{t_0^\frac{9}{4},1\}\|v_0\|^3_{L^2_{\textnormal{uloc}}(\mathbb{R}^3)} \right) =: C(1 + A(3r) + V_0),
	\end{align*}
	where we used H\"{o}lder, Young and Calder\'{o}n-Zygmund inequalities, a similar estimate for $p_2$ as in the proof of Thereom \ref{theo1} and \cite[Lemma 3.5]{KMT2020_2}. It can be seen that for $0 < 2r \leq \rho \leq r_0$
    \begin{equation*}
    	A(r) \leq C\left(\frac{r}{\rho}\right) A(\rho)  + C\left(\frac{\rho}{r}\right)^2 \frac{1}{\rho^2}\int_{Q_{\rho}(z_0)} |v-v_\rho|^3 \,dz  =: C\left(\frac{r}{\rho}\right) A(\rho)  + C\left(\frac{\rho}{r}\right)^2 \bar{A}(\rho).
    \end{equation*}
	\textbf{Case (i).} Similarly to \cite[Lemma A.2]{WZ2014}, by using H\"{o}lder and Poincar\'{e} inequalities we obtain
	\begin{equation*}
		\bar{A}(\rho) \leq CE(\rho)^\frac{3(\alpha+\beta)}{2} \left(\rho^{1-\frac{2}{p_0}-\frac{3}{q_0}}  \|v-v_\rho\|_{L^{p_0}_tL^{q_0}_x (Q_\rho(z_0))}\right)^{3(1-\alpha-\beta)} \leq CE(\rho)^\frac{3(\alpha+\beta)}{2} M^{3(1-\alpha-\beta)},
	\end{equation*}
	where $0 < \rho \leq r_0$, $\alpha$ and $\beta$ should satisfy $\alpha \geq 0, \beta \geq 0$ and
	\begin{align*}
		1 &= \frac{3\alpha}{2} + \frac{\beta}{2} + \frac{3(1-\alpha-\beta)}{q_0},
		\quad 1 = \frac{3\beta}{2} + \frac{3(1-\alpha-\beta)}{p_0}, \quad 1 > \alpha + \beta, \quad \frac{2}{3} > \alpha, \beta,
		\\
		\text{i.e., } \alpha &= \frac{2}{3} \left(\frac{3}{p_0} + \frac{3}{q_0} - 2\right) \left(\frac{4}{p_0} + \frac{6}{q_0} - 3\right)^{-1}, \quad \beta =  \left(\frac{2}{p_0} + \frac{4}{q_0} - 2\right) \left(\frac{4}{p_0} + \frac{6}{q_0} - 3\right)^{-1}.
	\end{align*}
	In order to ensure $\alpha,\beta \geq 0$, we need to restrict ourselves to the cases
	\begin{equation*}
		\frac{3}{2} < \frac{2}{p_0} + \frac{3}{q_0} < 2,\quad \frac{3}{p_0} + \frac{3}{q_0} \geq 2,\quad \frac{2}{p_0} + \frac{4}{q_0} \geq 2, \quad p_0,q_0 < \infty.
	\end{equation*}
	However, other cases follow by using H\"{o}lder inequality. Indeed, for $(p_1,q_1)$ such that $1 \leq \frac{2}{p_1} + \frac{3}{q_1} < 2$ with $\frac{3}{2} < q_1 \leq \infty$ we can find $(p_0,q_0)$ satisfying the above conditions and
	\begin{equation*}
		\rho^{1-\frac{2}{p_1}-\frac{3}{q_1}}  \|v-v_\rho\|_{L^{p_1}_tL^{q_1}_x (Q_\rho(z_0))} \leq C \rho^{1-\frac{2}{p_0}-\frac{3}{q_0}} \|v-v_\rho\|_{L^{p_0}_tL^{q_0}_x (Q_\rho(z_0))}.
	\end{equation*}
	In addition, we have $0 \leq 3(\alpha + \beta) < 2$ since our restriction on $(p_0,q_0)$.  By using the above estimates and Young inequality we find that for $0 < 3(\alpha + \beta) < 2$,
	\begin{align*}
		A(r) &\leq C\left(\frac{r}{\rho}\right) A(\rho)  + C\left(\frac{\rho}{r}\right)^2 \bar{A}(\rho) \qquad (0 < 2r \leq \rho \leq r_0)
		\\
		&\leq C\left(\frac{r}{\rho}\right) A(\rho) + C\left(\frac{\rho}{r}\right)^2 E(\rho)^\frac{3(\alpha+\beta)}{2} M^{3(1-\alpha-\beta)}
		\\
		&\leq C\left(\frac{r}{3\rho}\right) A(3\rho) + C\left(\frac{3\rho}{r}\right)^2 (C(1 + V_0 +  A(3\rho)))^\frac{3(\alpha+\beta)}{2} M^{3(1-\alpha-\beta)} \quad (0 < 6r \leq 3\rho \leq r_0)
		\\
		&\leq \left(\frac{C_0\theta}{3} + \frac{1}{4}\right) A(3\rho) + \theta^{-\frac{4}{2-3(\alpha+\beta)}} C_{\alpha,\beta,M,V_0}  \qquad (r = \theta\rho, 2\theta \leq 1)
		\\
		&\leq \frac{1}{2} A(3\rho) + \theta^{-\frac{4}{2-3(\alpha+\beta)}} C_{\alpha,\beta,M,V_0}  \qquad (4C_0\theta \leq 3, 2\theta \leq 1, 3\rho \leq r_0),
	\end{align*}
	where $C_0 > 1$ is an absolute constant, and for $\alpha + \beta = 0$ (i.e., $\alpha = \beta = 0$ or $p_0 = q_0 = 3$)
	\begin{equation*}
		A(\theta\rho) \leq \frac{1}{2} A(3\rho) + \theta^{-2} C_M, \qquad (4C_0\theta \leq 3, 2\theta \leq 1, 3\rho \leq r_0).
	\end{equation*}
	We choose $\theta = \min\{\frac{3}{4C_0},\frac{1}{2}\}$ and denote $\theta_0 = \frac{\theta}{3}$, $\rho_0 = 3\rho$. By iteration,
	\begin{equation*}
		A(\theta^k_0\rho_0) \leq \frac{1}{2^k} A(\rho_0) + C_{\alpha,\beta,M,V_0}, \qquad  \forall k \geq 1, 0 < \rho_0 \leq r_0.
	\end{equation*}
	Thus, there exists $k_0 = k_0(r_0)$ sufficiently large such that
	\begin{equation*}
		A(r) \leq  C_{\alpha,\beta,M,V_0,r_0}, \qquad \forall 0 < r \leq \theta_0^{k_0}r_0.
	\end{equation*}
	\textbf{Case (ii).} Similarly to the previous case, by using H\"{o}lder, Poincar\'{e} and Sobolev inequalities we find that
	\begin{equation*}
		\bar{A}(\rho) \leq CE(\rho)^\frac{3\gamma_0}{2} \left(\rho^{2-\frac{2}{p_0}-\frac{3}{q_0}}  \|\nabla v\|_{L^{p_0}_tL^{q_0}_x (Q_\rho(z_0))}\right)^{3(1-\gamma_0)} \leq CE(\rho)^\frac{3\gamma_0}{2} M^{3(1-\gamma_0)},
	\end{equation*}
	where $0 < \rho \leq r_0$, $\gamma_0 = \alpha_0 + \beta_0$, $\alpha_0$ and $\beta_0$ should satisfy $\alpha_0 \geq 0, \beta_0 \geq 0$ and
	\begin{align*}
		1 &= \frac{3\alpha_0}{2} + \frac{\beta_0}{2} + \frac{3(1-\alpha_0-\beta_0)}{q^*_0}, \quad q^*_0 = \frac{3q_0}{3-q_0} \quad \text{for} \quad q_0 \in (1,3),
		\\
		\quad 1 &= \frac{3\beta_0}{2} + \frac{3(1-\alpha_0-\beta_0)}{p_0}, \quad 1 > \alpha_0 + \beta_0, \quad \frac{2}{3} > \alpha_0, \beta_0,
		\\
		\text{i.e., } \alpha_0 &= \frac{2}{3} \left(\frac{3}{p_0} + \frac{3}{q_0} - 3\right) \left(\frac{4}{p_0} + \frac{6}{q_0} - 5\right)^{-1}, \quad \beta_0 =  \left(\frac{2}{p_0} + \frac{4}{q_0} - \frac{10}{3}\right) \left(\frac{4}{p_0} + \frac{6}{q_0} - 5\right)^{-1}.
	\end{align*}
	So that we force ourselves to the cases
	\begin{equation*}
		\frac{5}{2} < \frac{2}{p_0} + \frac{3}{q_0} < 3,\quad \frac{3}{p_0} + \frac{3}{q_0} \geq 3,\quad \frac{2}{p_0} + \frac{4}{q_0} \geq \frac{10}{3}, \quad q_0 \in (1,3)
	\end{equation*}
	and other cases can be recovered by using H\"{o}ler inequality as above. Note that we have $0 \leq 3\gamma_0 < 2$. Therefore, we can bound $A(r)$ as in  Case (i).
	\\
	\textbf{Case (iii).} Let $w = \nabla \times v$ and $0 < \rho \leq r_0$, as in \cite[Lemma 3.6]{GKT2007}, we define
	\begin{equation*}
		u(x,t) := \text{p.v.} \frac{1}{4\pi} \int_{\mathbb{R}^3} \nabla_x\left(\frac{1}{|x-y|}\right) \times w(y,t) \phi(y) \,dy \quad \text{and} \quad h := v - u,
	\end{equation*}
	where $\phi$ is a standard cut off function supported in $B_\rho(x_0)$ such that $\phi = 1$ in $B_{\frac{3\rho}{4}}(x_0)$. It can be seen that $\Delta h = 0$ in $B_{\frac{3\rho}{4}}(x_0)$. For $0 < 2r \leq \rho \leq r_0$ and $q_0 \in (1,\infty)$ we find that
	\begin{align*}
		\|\nabla v\|^{q_0}_{L^{q_0}(B_r(x_0))} &\leq C_{q_0} \|\nabla u\|^{q_0}_{L^{q_0}(B_r(x_0))} + C_{q_0} \|\nabla h\|^{q_0}_{L^{q_0}(B_r(x_0))}
		\\
		&\leq C_{q_0} \|w\|^{q_0}_{L^{q_0}(B_{\rho}(x_0))} + C_{q_0} \left(\frac{r}{\rho}\right)^3 \|\nabla h\|^{q_0}_{L^{q_0}(B_{\rho}(x_0))}
		\\
		&\leq C_{q_0} \|w\|^{q_0}_{L^{q_0}(B_{\rho}(x_0))} + C_{q_0} \left(\frac{r}{\rho}\right)^3 \|\nabla v\|^{q_0}_{L^{q_0}(B_{\rho}(x_0))},
	\end{align*}
	where we used the Calder\'{o}n-Zygmund estimate and the mean value property of harmonic functions. Integrating in time yields for $ 1 < q_0 < 3$ (other cases can be recovered by using H\"{o}lder inequality)
	\begin{align*}
		H(r) &:= r^{2-\frac{2}{p_0}-\frac{3}{q_0}} \|\nabla v\|_{L^{p_0}_tL^{q_0}_x(Q_r(z_0))}  \qquad (0 < r \leq r_0)
		\\
		&\leq C_{p_0,q_0} \left(\frac{r}{\rho}\right)^{2-\frac{2}{p_0}-\frac{3}{q_0}} M + C_{p_0,q_0} \left(\frac{r}{\rho}\right)^{2-\frac{2}{p_0}} H(\rho) \qquad (0 < 2r \leq \rho \leq r_0)
		\\
		&= C_{p_0,q_0} \theta^{2-\frac{2}{p_0}-\frac{3}{q_0}} M + C_{p_0,q_0} \theta^{2-\frac{2}{p_0}} H(\rho) \qquad (r = \theta \rho, 2\theta \leq 1, 0 < \rho \leq r_0)
		\\
		&\leq C_{p_0,q_0} \theta^{2-\frac{2}{p_0}-\frac{3}{q_0}} M + C_{p_0,q_0} \theta^{\frac{3}{q_0}-1} H(\rho) \qquad (r = \theta \rho, 2\theta \leq 1, C_{p_0,q_0} > 1, 0 < \rho \leq r_0)
		\\
		&\leq C_{p_0,q_0} M + \frac{1}{2} H(\rho) \qquad (2C_{p_0,q_0} \theta^{\frac{3}{q_0}-1} \leq 1, 2\theta \leq 1, C_{p_0,q_0} > 1, 0 < \rho \leq r_0).
	\end{align*}
	By iteration, we can bound $H(r)$ by $C_{p_0,q_0} M$ for $0 < r \leq \theta^{k_0}r_0$ with some sufficiently large integer $k_0(r_0)$. It returns to Case (ii).
	\\
	\textbf{Case (iv).} For $0 < 2r \leq \rho \leq r_0$, $1 \leq q_0 < \frac{3}{2}$ (other cases where $\frac{3}{2}\leq q_0 \leq \infty$ can be recovered by using H\"{o}lder inequality) and $\frac{3}{2} \leq \bar{q}_0 := \frac{3q_0}{3-q_0} < 3$, using Sobolev inequality yields
	\begin{align*}
	\|w\|^{\bar{q}_0}_{L^{\bar{q}_0}(B_r(x_0))} &\leq C_{q_0} \left(\frac{r}{\rho}\right)^3 \|w\|^{\bar{q}_0}_{L^{\bar{q}_0}(B_{\rho}(x_0))} + C_{q_0} \|w-w_\rho\|^{\bar{q}_0}_{L^{\bar{q}_0}(B_{\rho}(x_0))}
	\\
	&\leq C_{q_0} \left(\frac{r}{\rho}\right)^3 \|w\|^{\bar{q}_0}_{L^{\bar{q}_0}(B_{\rho}(x_0))} + C_{q_0} \|\nabla w\|^{\bar{q}_0}_{L^{q_0}(B_{\rho}(x_0))},
	\end{align*}
	which implies that
	\begin{align*}
		G(r) &:= r^{2-\frac{2}{p_0}-\frac{3}{\bar{q}_0}} \| w\|_{L^{p_0}_tL^{\bar{q}_0}_x(Q_r(z_0))}  \qquad (0 < r \leq r_0)
		\\
		&\leq C_{p_0,q_0} \theta^{\frac{3}{q_0}-2} G(\rho) + C_{p_0,q_0} \theta^{2-\frac{2}{p_0}-\frac{3}{q_0}} M \qquad (0 < \rho \leq r_0, r = \theta \rho, 2\theta \leq 1,C_{p_0,q_0} > 1)
		\\
		&\leq \frac{1}{2} G(\rho) + C_{p_0,q_0} M \qquad (2C_{p_0,q_0} \theta^{\frac{3}{q_0}-2} \leq 1, 2\theta \leq 1, 0 < \rho \leq r_0).
	\end{align*}
	Therefore, $G(r)$ is bounded by $C_{p_0,q_0} M$ for $0 < r \leq \theta^{k_0}r_0$ with some sufficiently large integer $k_0(r_0)$. We then return to Case (iii) since $\frac{2}{p_0} + \frac{3}{\bar{q}_0} = \frac{2}{p_0} + \frac{3}{q_0} - 1 \in [2,3)$. All above cases imply that
	\begin{equation*}
		E(r) \leq  C_{\alpha,\alpha_0,\beta,\beta_0,M,V_0,p_0,q_0,r_0}, \qquad \forall 0 < r \leq r_0.
	\end{equation*}
	The rest of the proof is similar to that of Theorem \ref{theo1} by using \eqref{v3z0} instead of \eqref{v3v0}, where we only need to modify the definition of $(v_\delta,\pi_\delta)$ in the following way
	\begin{equation*}
		v_\delta(x,t) := \delta v(\delta x + x_0,\delta^2 t + t_0)
		\quad
		\text{and}
		\quad
		\pi_\delta(x,t) := \delta^2 \pi_{r_0,x_0}(\delta x + x_0,\delta^2 t + t_0).
	\end{equation*}

	$\bullet$\,\textnormal{(}The case of suitable weak solution\textnormal{)}
	The local energy inequality yields for $0 < 2r \leq r_0$
	\begin{align*}
		E(r) &\leq C\left(1 +  \frac{1}{4r^2} \|v\|^3_{L^3(Q_{2r}(z_0))}  + \frac{1}{4r^2} \|\pi|^\frac{3}{2}_{L^\frac{3}{2}(Q_{2r}(z_0))}\right) =: C(1 + A(2r) + B(2r)),
	\end{align*}
	where $E(r)$ is given as in the case of local energy solutions with $\pi$ instead of $\pi_{r_0,x_0}$. As in \cite[Lemma 3.4]{GKT2007} we have
	\begin{equation*}
		B(r) \leq C\left(\frac{r}{\rho}\right) B(\rho) + C \left(\frac{\rho}{r}\right)^2 \bar{A}(\rho) \qquad \text{for} \quad 0 < 2r \leq \rho \leq r_0,
	\end{equation*}
	which imples as in the previous case that
	\begin{align*}
		D(r) &:= A(r) + B(r) \qquad (0 < 2r \leq r_0)
		\\
		&\leq C\left(\frac{r}{\rho}\right) D(\rho)   + C\left(\frac{\rho}{r}\right)^2 \bar{A}(\rho) \qquad (0 < 8r \leq 4\rho \leq r_0)
		\\
		&\leq C\left(\frac{r}{\rho}\right) D(\rho)  + C\left(\frac{\rho}{r}\right)^2 E(\rho)^\frac{3(\alpha+\beta)}{2} M^{3(1-\alpha-\beta)}
		\\
		&\leq C\left(\frac{r}{2\rho}\right) D(2\rho) + C\left(\frac{\rho}{r}\right)^2 (C(1 + D(2\rho)))^\frac{3(\alpha+\beta)}{2} M^{3(1-\alpha-\beta)}.
	\end{align*}
	The rest of the proof then can follows as in the case of local energy solutions by considering $D(r)$ as $A(r)$. We omit the details and end the proof.
	\end{proof}

	%

	\section{Proof of Theorem \ref{theo3}}\label{sec:theo3}

	%

	We will present the proof of Theorem \ref{theo3}.
	The idea of the proof comes from those of \cite[Theorems 2.1]{KWM2017,KWM2019}. However, for local energy solutions the condition is not involved the pressure due to the decomposition \eqref{pressure_decomposition}.

	\begin{proof}[Proof of Theorem \ref{theo3}]\quad $\bullet$\,\textnormal{(}The case of local energy solution\textnormal{)}\, We assume that the conclusion is not true, i.e., there exists a sequence of local energy solutions $(v^n,\pi^n)$ such that
	\begin{equation*}
	\left\{
	\begin{aligned}
		r_0^{-2} \|v^n\|^3_{L^3(Q_{r_0}(z_0))}  &\leq M,
		\\
		r^{1-\frac{2}{p}-\frac{3}{q}}_0 \|v^n_3\|_{L^p_tL^q_x(Q_{r_0}(z_0))} &\to 0 \qquad \text{as}\quad n \to \infty \quad \text{for} \quad 1 \leq p,q \leq \infty,
		\\
		(\delta_0 r_0)^{-2} \|v^n\|^3_{L^3(Q_{\delta_0 r_0}(z_0))} &> \epsilon_0 \qquad \forall \delta_0 \in (0,1).
	\end{aligned}
	\right.
	\end{equation*}
	As in the proof of Theorem \ref{theo2},
	\begin{equation*}
		E^n(r) \leq C(1 + M + V_0) \qquad \text{for} \quad r := \frac{r_0}{3},
	\end{equation*}
	where $E^n(r)$ is given as in the proof of Theorem \ref{theo2} with $(v^n,\pi^n_{r_0,x_0})$ instead of $(v,\pi_{r_0,x_0})$. Therefore, there exist a subsequence of $(v^n,\pi^n_{r_0,x_0})$ (still denoted by $(v^n,\pi^n_{r_0,x_0})$) and $(\bar{v},\bar{\pi})$ such that as $n \to \infty$
	\begin{equation*}
		\left\{
		\begin{aligned}
			v^n  &\overset{\ast}{\rightharpoonup} \bar{v} \qquad \text{ in } L^\infty_tL^2_x(Q_{r}(z_0))),
			\\
			\nabla v^n  &\overset{}{\rightharpoonup} \nabla \bar{v} \quad\, \text{ in } L^2(Q_{r}(z_0)),
			\\
			\pi^n_{r_0,x_0}  &\overset{}{\rightharpoonup} \bar{\pi} \qquad \text{ in } L^\frac{3}{2}(Q_{r}(z_0)),
			\\
			v^n &\to \bar{v} \qquad \,\,\text{in } L^a(Q_{r}(z_0)) \qquad \text{for} \quad 1 \leq a < \frac{10}{3}.
		\end{aligned}
		\right.
	\end{equation*}
	In addition, we have $(\bar{v},\bar{\pi})$ is a suitable weak solution to \eqref{NS} in $Q_{r_0}(z_0)$. The convergence of $v^n_3$ implies that $\bar{v}_3 \equiv 0$. Therefore, $(\bar{v},\bar{\pi})$ is also a suitable weak solution to "the limiting system" and $\bar{v}$ is regular as well. Taking $n \to \infty$ yields
	\begin{equation*}
		(\delta_0 r)^{-2} \|v^n\|^3_{L^3(Q_{\delta_0 r}(z_0))} \to (\delta_0 r)^{-2} \|\bar{v}\|^3_{L^3(Q_{\delta_0 r}(z_0))} \geq \epsilon_0 \qquad \forall \delta_0 \in (0,1),
	\end{equation*}
	which is a contradiction with the regularity of $\bar{v}$ for $\delta_0$ small enough. Therefore, the proof is complete.

	$\bullet$\,\textnormal{(}The case of suitable weak solution\textnormal{)} The proof in this case is similar to that of for local energy solutions. We define $E^n(r)$ as in the proof of Theorem \ref{theo2} with $(v^n,\pi^n)$ instead of $(v,\pi_{r_0,x_0})$. Thus,
	\begin{equation*}
		E^n(r) \leq C(1 + M) \qquad \text{for} \quad r := \frac{r_0}{2},
	\end{equation*}
	that completes the proof as in the previous case.
	\end{proof}

	%

	\section*{Acknowledgments}

	%
	K. Kang was supported by NRF-2019R1A2C1084685.
    D. D. Nguyen was supported by NRF-2015R1A5A1009350.

redpajama_set_name: RedPajamaArXiv


Fri., January 15, 2016 11:40 p.m. | Friday, January 15, 2016 11:40 p.m.
Allegheny County District Attorney Stephen A. Zappala Jr. on Friday said he notified Bridgeville Councilman Jason Sarasnick that a criminal conviction precludes him from continuing to serve.
Zappala said his office gave Sarasnick, 46, seven to 10 days to resign.
"My understanding is that he intends to resign," Zappala said.
Sarasnick did not return messages seeking comment.
Allegheny County court records show Sarasnick pleaded guilty in 1992 to a felony charge of manufacture, delivering or possessing with intent to deliver a controlled substance, and a misdemeanor charge of intent to possess a controlled substance. He was sentenced to a minimum of 11 months' confinement.
Sarasnick, a Republican, was re-elected to council in November, having served since at least 2008, according to county election records. He was the top vote-getter among six candidates for three council seats, and he is president of Sarasnick Brothers Hardware on Washington Avenue in Bridgeville.
The district attorney's office said it looked into Sarasnick's record based on a tip.
Zappala's office recently informed Corey Sanders, 45, that he cannot take the McKeesport council seat to which he was elected in November because of a 23-year-old drug conviction.
Bridgeville Mayor Pasquale DeBlasio and Manager Lori Collins could not be reached for comment.
The next Bridgeville council meeting is at 7 p.m. Feb. 8.
Staff writer Jason Cato contributed. Jim Spezialetti is a Tribune-Review staff writer.


What constitutes Teshuvah? That a sinner should abandon his sins and remove them from his thoughts, resolving in his heart, never to commit them again as [Isaiah 55:7] states "May the wicked abandon his ways...." Similarly, he must regret the past as [Jeremiah 31:18] states: "After I returned, I regretted."
[He must reach the level where] He who knows the hidden will testify concerning him that he will never return to this sin again as [Hoshea 14:4] states: "We will no longer say to the work of our hands: `You are our gods.'"
He must verbally confess and state these matters which he resolved in his heart.
resolve never to repeat that sin.
There is no specific method of teshuvah for specific sins. It certainly helps to study the halochos related to the sin.
[Who has reached] complete Teshuvah? A person who confronts the same situation in which he sinned when he has the potential to commit [the sin again], and, nevertheless, abstains and does not commit it because of his Teshuvah alone and not because of fear or a lack of strength.
The answer did not specifically address the part of the the question relating to non-Jews.
…... non-Jews can and must perform teshuvah.
We explained that there is a basic level of teshuvah, which is simply the decision to not sin again. Thereby, one may be considered a "righteous person" from the time this teshuvah is performed and thereafter. Then there is a higher level of teshuvah, consisting of regretting the sins, confession, and in certain cases, other factors as well.
It is the first category of teshuvah that applies to non-Jews, as well as to Jews. If they have sinned, they must make efforts to change their ways and desist from sinning in the future. Indeed, by doing so they may spare themselves from punishment, as was the case with the people of Nineveh. They are not, however, afforded the special opportunity to rectify the past through regret and confession, thereby wiping the slate clean. According to this approach, this more complete form of teshuvah is reserved for the Jewish people only. This distinction can be understood based on an explanation given by Rabbi Moshe Di Trani, in his work Beit Elokim: Since Jews have six hundred and thirteen mitzvot, it is expected that at times Jews will succumb to sin. Non-Jews, on the other hand, only need to observe seven mitzvot and as such are expected not to fail in their observance in the first place.
…... it is possible that Righteous gentiles actually fall in the same category as Jews with regard to Teshuva and can also reach the higher level of teshuva which wipes the slate clean.
So the non-Jew must try to change and stop sinning in the future. It seems that it may be possible for him to go further and follow the same prescriptions that the Rambam lays down for Jews.
In short, there's no Teshuvah for non-Jews. And please don't kill the messenger (me).
"The Jerusalem Talmud, Nazir, beginning of Chapter 9. as well as the Midrash Tanchuma Parshat Haazinu, 4 seem to indicate that while Teshuvah atones for a Jew's sins, it does not atone for the sins of a non-Jew."
The Jewish system of Mitzvos is very different from the system of non-Jews, for example, Jews are not punished for all monetary misdeeds (theft, wage withholding etc) as they all can be repaid (paid back later), but a non-Jew who stole a thing is capitally punished and he can not return the theft to undo his sin (Rambam Melachim).
Same with Teshuva, sorry to disappoint you, it is reserved for the Jews only (it is also a positive Mitzvah). So a Jew can [theoretically] fix his misdeed by doing Teshuva (described in Rambam for example), but a non-Jew that sinned has no such option.
Both Jews and non-Jews can decide to stop sinning in the future, but this does not annulate what's already done per se.
"עבר על כריתות ומיתות בית דין ועשה תשובה תשובה ויוה"כ תולין ויסורין הבאין עליו גומרין לו הכפרה ולעולם אין מתכפר לו כפרה גמורה עד שיבואו עליו יסורין"
"If a person violates sins punishable by karet or execution by the court and repents, Teshuvah and Yom Kippur have a tentative effect and the sufferings which come upon him complete the atonement. He will never achieve complete atonement until he endures suffering for concerning these sins..."
On the positive side, he can always convert and start a new life with a new Jewish soul that automatically annulates all his non-Jewish sins. Well, not really annulates, it's just a brand new soul, so I have no idea what happens to the old non-Jewish soul.
Not the answer you're looking for? Browse other questions tagged repentance-teshuvah noachide-laws .


text:
In this successful history, journalist Nagorski isolates 1941 as a turning point in world history, persuasively arguing it was the year Adolf Hitler's political and military decisions ensured the downfall of the Third Reich. A year that began with the Soviet Union and Germany carving up occupied Poland, while British prime minister Winston Churchill tried to inveigle the United States to enter the war, ended with Russia, Britain, and the U.S. allied against Germany. As Nagorski recounts, 1941 was the year of "Germany's attack on the whole world." Hitler's uneasy nonaggression pact with rival tyrant Josef Stalin came apart with the June 22 German invasion of the Soviet Union. Stalin ignored warnings of the attack from his generals, well-placed spies, and U.S. diplomats, nearly allowing Hitler's prediction that a "swift victory over Russia was all but inevitable" to come true. Hitler, meanwhile, erred in committing to support Japan if it came to war with the U.S.; the December 7 attack on Pearl Harbor cemented a tripartite alliance that destroyed the Axis powers. Nagorksi's strength is in piecing together political, diplomatic, and military narratives to create a cohesive whole. He's a clear and lucid writer whose account of this pivotal year will please history buffs. Agent: Robert Gottlieb, Trident Media Group. (June)
A fresh look at the decisive year 1941, when Hitler's miscalculations and policy of terror propelled Churchill, FDR, and Stalin into a powerful new alliance that defeated Nazi Germany.
Buy at:


We were created after Galvano yelled at The Moon before 2015. The moon, inorganic entity of light is here to teach us the lunatik side of the subconscious mind. A sound projection that you can witness from Galvano's guitar solo.


Ed Stetzer, president of LifeWay Research, appeared on CNN's Situation Room to discuss online scams targeting Rick Warren as the Saddleback Church pastor and his family grieve the death of his son Matthew.
Since his son's suicide in April, more than 200 fake Rick Warren Facebook pages appeared and began to solicit funds. The scammers claimed the donations would go to the Matthew Warren Fund, which the family established to fight mental illness.
179 of over 200 FAKE Rick Warren Facebook pages created by scammers to make money on my son's death have now been shut down. We're still working on the rest. Thanks to you friends for reporting them and thanks for "LIKING" this real page. I appreciate you so much for your help. God bless you.
According to Stetzer, it is an all too common occurrence. "People see the name and they click "Friend" or "Like" and then the criminals begin to reach out to people who are trusting that they are hearing from a trusted Christian leader." A 2011, LifeWay Research study found churches are increasingly using Facebook to communicate with their members, with 47 percent of Protestant churches regularly using the social media site.
Prior to his return to the pulpit at Saddleback, Warren dealt with the recent crop of counterfeit Facebook pages, as well as someone hacking his Twitter account. Warren praised Twitter officials for responding quickly to restore control of his Twitter account.
Stetzer is familiar with fake social media accounts, as he has dealt with his own. He said the scammers copy photos of the individual they are seeking to mimic in order to make their page seem legitimate. On his fake Facebook page, people began to notice that something seemed off.
Facebook, Twitter and other social media sites can deal with fake accounts seeking to pass themselves off as real or acting maliciously. Users simply need to report them and continue to be on guard for those seeking to exploit emotions for financial and personal gain.


text:
Q: Windows XP IIS 5.1 MetaBase corrupted somehow, reinstalling doesn't help Somehow my MetaBase.bin is corrupted on my Windows XP machine. I've attempted to uninstall and reinstall IIS numerous times. I did see the Reinstalling IIS on WinXP machine post here which I made sure to follow exactly however after uninstalling IIS the Inetserv folder does not get completely removed it is left with.
MetaBase.bin aqadmin.dll aqueue.dll seos.dll
Anytime I delete those files they immediately reappear.
When I attempt to reinstall IIS I am presented with:
iis6.log
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:ProcessSection.[register_iis_core_dcom].Start.
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=74...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=76...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=86...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:Calling ProcessSection:register_iis_core_dcom:End.return=1
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=47...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:ProcessEntry_If:check if [51=6]
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=5...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:Calling ProcessSection:register_iis_core_fillmetabase:Start.
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:ProcessSection.[register_iis_core_fillmetabase].Start.
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=106...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:SetAdminACL:(/)Start.
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:SetAdminACL:Write the new security descriptor to the Metabase:Start.
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:SetAdminACL:  At this point we have already been able to write basic entries to the metabase, so...
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:SetAdminACL:  If this has a problem then there is a problem with setting up encryption for the metabase (Crypto).
[3/10/2010 19:3:2] OC_COMPLETE_INSTALLATION:iis_core:WriteSDtoMetaBase:Start.
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:MyMessageBox: Title:IIS Setup Error, Msg:CoGetClassObject

0x80080005=Server execution failed

[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:WriteSDtoMetaBase:End.  Return=0x80080005
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:SetAdminACL:Write the new security descriptor to the Metabase:End.
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:SetAdminACL(/):End.
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:MyMessageBox: Title:IIS Setup Error, Msg:Do you want to retry?
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=86...
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=2...
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:------------------
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:CallProcedureInDll(C:\WINDOWS\system32\inetsrv\iislog.dll): DllRegisterServer
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:iOleInitialize: Succeeded: 0.  MakeSure to call OleUninitialize.
[3/10/2010 19:3:32] OC_COMPLETE_INSTALLATION:iis_core:CallProcedureInDll: Calling 'DllRegisterServer'.Start
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:MyMessageBox: Title:IIS Setup Error, Msg:Error calling procedure 'DllRegisterServer()' in file 'C:\WINDOWS\system32\inetsrv\iislog.dll'.

0x8000ffff=Catastrophic failure

[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:!FAIL!
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:CallProcedureInDll: Calling 'DllRegisterServer'.End.FAILED. Err=8000ffff.
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:------------------
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:MyMessageBox: Title:IIS Setup Error, Msg:Do you want to retry?
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=86...
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=84...
[3/10/2010 19:4:3] OC_COMPLETE_INSTALLATION:iis_core:MigrateInfSectionToMD:(CORE_REG_IIS3_UPGRADE)Start.
[3/10/2010 19:4:33] OC_COMPLETE_INSTALLATION:iis_core:MyMessageBox: Title:IIS Setup Error, Msg:CoGetClassObject

0x80080005=Server execution failed

[3/10/2010 19:4:33] OC_COMPLETE_INSTALLATION:iis_core:MigrateInfSectionToMD(CORE_REG_IIS3_UPGRADE):End.
[3/10/2010 19:4:33] OC_COMPLETE_INSTALLATION:iis_core:...ProcessEntry:100=84...
[3/10/2010 19:4:33] OC_COMPLETE_INSTALLATION:iis_core:MigrateInfSectionToMD:(CORE_REG)Start.
[3/10/2010 19:5:3] OC_COMPLETE_INSTALLATION:iis_core:MyMessageBox: Title:IIS Setup Error, Msg:CoGetClassObject

0x80080005=Server execution failed

And in the event viewer
Event ID: 7023
The IIS Admin service terminated with the following error:
The data is invalid.
Event ID: 10010
The server {A9E69610-B80D-11D0-B9B9-00A0C922E750} did not register with DCOM within the required timeout.

A: Looks like the problem occurred when trying to write the Cryptographic information in the Metabase i.e. iis_core:WriteSDtoMetaBase:Start. I suggest you uninstall IIS. Rename the MachineKeys i.e. machinekeys those are starting with c23 and 7a4. Then try reinstalling IIS.Hope this helps.

A: System restore actually worked to resolve this... surprisingly.

redpajama_set_name: RedPajamaStackExchange


text:
Kids Off The Streets Campaign
The Los Angeles FC Barcelona Soccer Foundation
The L.A. FC Barcelona Soccer Foundation 501(c)(3) was created to promote a social model that supports the achievement of social, cultural, and educational programs for underprivileged youth through our Soccer Academy KIDS OFF THE STREETS. These programs, on their own or as part of collaborations, allow us to fulfill our social commitment not only nationally but internationally as well. In that spirit, the message must be clear, education is the gateway to their future.
Participation in youth sports improves academic performance, increases self confidence, and promotes health and well being. Children who take part in team sports are more likely to finish high school and attend college while simultaneously far less likely to suffer from childhood obesity and related diseases.
In Los Angeles today, however, more than 25% of school-aged children are living below the poverty line. Creating opportunities for these children to rise above the cycle of poverty and achieve success in life represents a crucial need.
"Kids Off The Streets" was formed to ensure the many benefits of team sports are provided to the children who need them most. Through the program, children participate in soccer coached by skilled and caring professionals, in a structured format and setting, all completely free of charge. Today, most team sports for school-aged children require costly fees to participate; "Kids Off The Streets" covers all costs, including equipment, professional coaches, and state-of-the-art facilities. Removing the economic barrier, "Kids Off The Streets" ensures that no child is denied the opportunity to play team sports because they cannot afford the expense.
Support children who are at risk of being left behind
Encourage healthy lifestyles and academic achievement
Promote teamwork that fosters the values of sportsmanship
Ensure a safe harbor for youth, providing a secure and nurturing environment through high-quality athletic facilities and caring supervision
ACCOMPLISHMENTS:
Over 5000 children in Los Angeles have participated and benefited from the program.
Many players have matriculated to the college level.
Highly respected soccer clubs around the world have awarded training opportunities to our youth.
The primary goal of the program is growth. Our experience thus far has shown the strong benefits of our unique program and the impact it has had for the youth we have served. Our vision is to continue to expand our programs, enabling our ability to reach more children across the community.
Paul Walker chose to follow his dream of pioneering a new path in the world of youth soccer by forming a powerful association with FC Barcelona. As an official FCB "Supporters Club" (Official FCB Penya #1437), Walker's club gained access to a wealth of resources from the Spanish giant. So famous, Barça, as the professional football club is often referred to is based in Barcelona, Catalonia, Spain and was founded in 1899.
Paul Walker Executive Director | LA FC Barcelona Soccer Foundation
Rob Aigner is the General Manager for a group of 9 Keller Williams Realty offices from Northern to Southern California. Rob is also the owner operator of the Keller Williams Santa Barbara and the Bakersfield office. Rob has earned ownership in eight other Keller Williams offices and travels the country teaching as a certified KW faculty member and an active MAPS coach.
Rob Aigner Owner Operator Keller Williams
In 2007 Stuart founded IM Global, one of Hollywood's leading independent production, financing, international sales and distribution companies. The company is based in Los Angeles and has offices in New York, London, Beijing, Shanghai, Mumbai, Munich and Mexico City. In 2015 Ford was awarded the annual Achievement in International Film Award by Variety.
Stuart Ford Chief Executive Officer, AGC Studios
Juan Galvan is Co-Owner of Amapola Deli & Market. Amapola is a family-owned chain of grocery stores in and around Los Angeles County where their first store opened in 1961. Amapola Deli & Market has gained its fame and notoriety by selling the best corn tortillas and masa for tamales in Southern California. Amapola Departments Include: Tortillas, Meat & Seafood, Bakery, Deli & Produce. Juan is also President of Amapola Mexican Grill located in Downey, California.
Juan Galvan Co-Owner La Amapola Inc.
James has worked in the Los Angeles area for 20 years consulting in the financial services industry. He also owns and operates a real estate investment company and is involved in local lifestyle brands. James and his wife Donna live in Manhattan Beach together with their 3 children. James was an avid soccer player as a young man and has a true passion for the game. He now enjoys watching his children play and is an active volunteer in youth sports programs.
James Maertz Director at Wisdom Tree Asset Management
In Los Angeles today, more than 25% of school-aged children are living below the poverty line. Creating opportunities for these children to rise above the cycle of poverty and achieve success in life represents a crucial need.
Kids Off The Streets
admin@totalfutbolacademy.com
Copyright © 2021 Kids Off The Streets. All Rights Reserved.


text:
Inkcarceration Festival 2019 Preview
Friday, 5th July 2019 By Kyle McGinn
With all of the growing number of summer festivals, even here in the United States, it can be hard to stick out. But when you have your festival at the Ohio State Reformatory, the site of the film The Shawshank Redemption, it gives you some room to be different. In addition to this, the festival also focuses on tattoo artistry as much as it does music – a fine matchup for those fans of heavier music in general. With now one week to go before the second Inkcarceration Festival is to be held, we talked with one of the fests co-producers, Susan Fisher, to get some insight as to how something like this comes together from the ground up.
Dead Rhetoric: Where did the initial idea for the festival come from?
Susan Fisher: The Ohio State Reformatory had dabbled in this area, and they reached out to someone on my team and we pulled together a group of people who had been in music, production, food service, and marketing to make a core team to make it happen. We had folks in the music business who were able to contact the artists so that we could kick off last year with a pretty extraordinary first year line-up, and then we were off to the races?
Dead Rhetoric: What do you feel makes the festival stand out compared to some of the other summertime fests?
Fisher: We are festival people – we love it all. We love to go to everyone else's [festival], as time allows. I think our approach has been that there are plenty of weekends in the year and plenty of festival fun to go around. We just wanted to create an experience that is special and unique to us. Inkcarceration is like no other festival that you can go to on the planet. It takes place on the grounds of a 100+ year old landmark prison yard, where one of the most famous films [The Shawshank Redemption] was made and where you can enjoy 30 bands over the course of 3 days and get a tour of all of the Shawshank memorabilia. We also have 70 tattoo artists from around the world, who do extraordinary art, and we get to showcase them with a competition. It's just a trifecta – we are in a prison yard with rock music for three days and have tattoos in the background. We feel we have a pretty unique formula.
Dead Rhetoric: Given that this is the second time around, did you purposely change anything around or expand upon?
Fisher: We want to surprise and delight our fans with the best line-up every year, so that was the #1 focus this year – to make things bigger and better. So far by the response, we are quite pleased that everyone is looking forward to enjoying that. It's going to be hot in July [laughs], so we have a whole new food truck city area with a big huge tent where people can enjoy some awesome, gourmet food truck food, have a beverage, and just get out of the sun for a little bit. Keeping everyone comfortable, honestly, is a big priority given how hot it always is the second week in July. We've got misting stations, hydration stations, relaxing areas, you can go inside the brick prison which is much cooler than outside, or you can just hang out in this cool new Inkcarceration blankets. You can find a spot of land and just chill and enjoy the sunshine and listen to the music.
Dead Rhetoric: Could you talk about the "Escape from Blood Prison" haunted house event.
Fisher: That is in partnership with the Ohio State Reformatory – it's actually a feature that my friend, Vic Amesquita, puts on in the fall. We are basically bringing Halloween into July. Escape from Blood Prison will be one half of the cell block, with characters that are escaping. They are all dressed in character. You can get a ticket for this extra special feature – the tour of the prison is free with your Inkcarceration ticket, but Escape from Blood Prison is an extra feature. They do a few shows throughout the day, but when they are not in a show, they wander the festival and they can totally take you by surprise. They might tap you on the shoulder as you are getting a beer or something! They are frightful, I'm not going to lie [laughs]! They caught me off-guard a few times! It's a pretty cool element. It adds a level of mystique. When you see zombies and people with half-blown off faces coming out of these prison cells. It's pretty cool!
Dead Rhetoric: Could you discuss the money that was made for charities – is that something continuing this year?
Fisher: Absolutely – we've got partners throughout Mansfield, Ohio and Richland County, to even as far as Columbus and Cleveland, who are coming in and raising money for their charities. We have a number of good groups. That's also a priority for us. It's our way to sort of give back to the community. Our volunteers come in and get a free t-shirt, enjoy the music, and raise some money with their bar tips. Everyone remember to tip your bartender – the tips don't go to the bartender, they go to charity.
Dead Rhetoric: Is it important that you are pushing the local aspect, particularly with the food available?
Fisher: I think the food trucks come from a bit of a wider area – some of them are local. The objective there was to really bring in a great mix of gourmet food truck foods. We've got a great guy, Chas Kaplan, who runs the food truck festival in Columbus who is coming up to manage it. He has helped us source some awesome food. We will have everyone's favorite island noodles, Graeter's ice cream, and there will be a great mix of types of home-grown food truck food.
Dead Rhetoric: How do you go about the selection of bands and tattoo artists?
Fisher: Both of them are a bit of a juggling match. From the band standpoint, we have our wishlist every year. That's a matter of having the right price and getting the timing to align. If these bands are at Inkcarceration, they are on tour, which means you have to work around their tour schedule, but thankfully we have some that are working around us – we knew we were going to do year 2 early and the bands that came last year had a really good experience. Our phones starting ringing, which was a nice twist.
For the tattoo artists, the waiting list is long to get in. We wish we could accommodate everyone. There are obviously health standards that you have to meet. You can't just put tattoo artists anywhere, so we have dedicated parts of the prison. It's a very selective process, and my manager Mike's area of expertise – he is covered head to toe in tattoos. I'm not sure how he decides – but it has to do with timing too, so get your paperwork in early! You have to be licensed and of course that sort of stuff. He sources the best of the best from around the country. I know he is getting a piece done by an artist from Florida to get Andy Dufresne on his forearm. He already has the Reformatory his shoulder. You have to admire that commitment!
At around 8PM every night, there are three judges and 10 categories, and the artists will show off and enter the competition to be best in show, best black and grey, or best color – categories like that. It's a really fun aspect. The winners will be announced on the big stage, so it's fun for everybody. Not everyone is into getting inked or having appointments done, but you can always appreciate a good artist. So we let everyone in on the experience by showing the winners to the crowd.
Dead Rhetoric: So is the competition done at night or something they do during the day and you just see the finished product?
Fisher: It's right then. I don't know how many contestants there are per category, but the artists will submit their best work. Let's say they worked on a girl's hip and it was a color piece, then they would submit into that category. There's a crowd of 1000 people as the subject gets up there and shows off his or her art. The judges are right there – even if they are a little swollen still, they are judging live.
Dead Rhetoric: Was it validating to win the Tourism Award of Excellence?
Fisher: Yes – that was quite the honor, especially after just one year. Mansfield is a really beautiful and quaint town tucked between Cleveland and Columbus and there's a lot of really cool stuff that goes on here. But Inkcarceration at the Ohio State Reformatory is probably the biggest weekend. It did a lot for the local hotels and restaurants, and we sourced a lot of local suppliers – whether it was port-a-johns or the generators needed for the stage. The tents where all put up by a local company. We are very conscious about the community we are in, and giving back the business. We don't just bring in people from Cleveland or Columbus. Sometimes we have to, but we always source locally first if we can. So it was nice for them to recognize that. It was quite an honor.
Dead Rhetoric: What sort of behind the scenes legwork is necessary to get a festival of this size off the ground and running?
Fisher: You just go from 6AM or midnight and you have to think of the interactions with our guests every single step of the way. From when they plug in our parking lot into their GPS to when they arrive and how they are welcomed – there's an incredible amount of details. Especially in a small town, just figuring out where everyone parks. We have campers at the Richland County Fairgrounds, so we have shuttles going back and forth all day long. I had a 2 hour meeting today to make sure that the bus was running on a good schedule with the best route. Getting the people back to their campsite as efficiently as possible. There's a lot of operations and a lot of management. We are very focused on our collective team's festival experience – we want to treat others the way we want to be treated as a festival. That's our goal and guiding principle. We know that if we do that, we are going to do right by our festival guests. We think of everything and every detail, or at least we try to [laughs]! There's always something that you don't think of or doesn't go quite right but we try to keep it to a minimum.
Dead Rhetoric: What are your long term goals for the fest?
Fisher: I think we see this as a staple of if you like rock music, build in a weekend in Mansfield at Inkcarceration into your summer plans. We hope to make the event better every year, and have it be something that people just look forward to as, "I don't want to miss that." That's our dream state. It's an event that you don't want to miss. Being in that prison yard, surrounded by chain-link fence, with this ominous, gothic massive prison as a backdrop – it's the coolest feeling. We just want to show everyone a good time, with the best music we can bring to Mansfield and make it into something everyone looks forward to year after year.
Order tickets for Inkcarceration 2019
Inkcarceration Festival official website
Inkcarceration on Facebook
Turilli/Lione Rhapsody – Stepping Forward
Belzebubs – Heeding the Blackened Call
Sabaton – Thrill of the Kill
FirstBourne – Pick Up the Torch (Self-Released)
Thy Art is Murder – Human Target (Nuclear Blast)
Nightrider – Rock Machine (Self-Released)
Cwn Annwn – Patron Saint (Self-Released)
Aphrodite – Lust and War (Fighter Records)
Flotsam and Jetsam, Cloven Hoof, Vicious Rumors – May 24, 2019 – The Chance Theater, Poughkeepsie, NY
Metal Church/Doro – May 9, 2019 – The Chance Theater, Poughkeepsie, NY
The Three Tremors – March 1, 2019 – The Chance Theater, Poughkeepsie, NY
Antichrist – March 2, 2019 – The Abyss Festival, Gothenburg, Sweden
© 2013 - 2019 deadrhetoric.com


text:
Twitter co-founder Jack Dorsey will step down from his executive role at the social media platform
ByThe Associated Press
SAN FRANCISCO -- Twitter co-founder Jack Dorsey will step down from his executive role at the social media platform.


text:
The University of Canterbury (Māori: Te Whare Wānanga o Waitaha; postnominal abbreviation Cantuar. or Cant. for Cantuariensis, the Latin name for Canterbury) was initiated and founded by scholars from the University of Oxford in 1873 and is New Zealand's second-oldest university. It operates its main campus in the suburb of Ilam in the city of Christchurch, New Zealand. It offers degrees in Arts, Commerce, Education (physical education), Engineering, Fine Arts, Forestry, Law, Music, Social Work, Speech and Language Therapy, Science, Sports Coaching and Teaching.
Read more about University Of Canterbury: Campus, Organisation, Rankings, League Tables, Personnel, Student Association and Traditions, History, Coat of Arms, Awards, Notable Staff, Notable Alumni
Famous quotes containing the words university of, canterbury and/or university:
"Poetry presents indivisible wholes of human consciousness, modified and ordered by the stringent requirements of form. Prose, aiming at a definite and concrete goal, generally suppresses everything inessential to its purpose; poetry, existing only to exhibit itself as an aesthetic object, aims only at completeness and perfection of form."
—Richard Harter Fogle, U.S. critic, educator. The Imagery of Keats and Shelley, ch. 1, University of North Carolina Press (1949)
"Thou hast brought him a pardon from good King John.""
—Unknown. King John and the Abbot of Canterbury (l. 108)
"The scholar is that man who must take up into himself all the ability of the time, all the contributions of the past, all the hopes of the future. He must be an university of knowledges."
Terms related to university of canterbury:
Canterbury College
Field Station
Ilam Apartments
Sonoda Christchurch Campus


The Kansas City Athletics amateur side will attempt to qualify for their 2nd straight US Open Cup and 3rd in the last 4 years when they take the field tomorrow afternoon against the Dearborn Stars out of Michigan. The game tomorrow at noon at Olathe North high school is one of two Region II semifinals (the other taking place today in Chicago between RWB Adria and FC Indiana). The winners of the two games will qualify for the US Open Cup proper along with earning themselves a birth in the Region II finals.
The Athletics advanced to the semifinals with a win over FC Indiana a few weeks ago by a 3-1 score line (the 1 goal scored by Indiana was enough to see them through to the semifinals as the "best loser"). Goals by Brian Williams, Matt Kuhn, and Garrett Webb helped the Athletics to a win over an Indiana side that was looking to be the "best loser" by the way they came out to play. For Dearborn, they easily dispatched the Cincy Saints 5-0 to advance in their game.
So get out to Olathe North tomorrow and cheer on a local side looking to qualify for the 100th edition of the US Open Cup.
2nd sentence, it says noon.


I can't wait to read your next Holmes!
Some research has shown that Moses married his half sister Nefertiti and their son was Tutankhamen. Akhenaten (Amenhotep IV) was forced to abdicate due to his faceless "Aten" God. Moses is also said to have been the son of Joseph's (Chief minister to Amenhotep III) daughter Tiye. Sounds interesting. Is it true?
In this way, the team was able to determine that a mummy known until now as KV55 is the "heretic king" Akhenaten—and that he was King Tut's father. Akhenaten was best known for abolishing ancient Egypt's pantheon in favor of worshipping only one god. The big surprise of the DNA analysis was the revelation of the identity of Tutankhamun's mother, as it showed that the other unidentified female mummy from Amenophis II's tomb, known as the 'Younger Lady' was the woman who gave birth to him. It also showed that this unnamed royal lady was one of the daughters of Amenophis III and Tiye, and therefore the sister of Akhenaten.
I knocked on the door of Ye Duzhuang's apartment at the Academy of Agricultural Sciences compound on Beijing's northwest edge.
Ye answered the door himself. Before me stood a tall man, over six feet, lean, with jet black hair above a calm face with a strong nose. He was 70 years old, but still alert, and moved with little trace of his age.
Fascinating! I would like to think China is softening but apparently not.
Lucky to see an Elk that close, but I'm sad to hear about the chains wrapped around his horns. We don't realize how often our garbage messes with wildlife.
Great read Ray! Thoroughly enjoyed with a tinge of jealousy mixed in. I would love to see Al's photos of this trip. Possible for a link?
Last week's entry made if a full year I've had the privilege of posting weekly essays under the broad rubric of Living and Writing in the Natural World. It's been a blast, and much of the enjoyment has been the feedback from those of you following my (mis)adventures.
Half dome behind the oak--shrouded in smoke!
My long-planned Yosemite outing this past weekend would be perfect: Amtrak bus and train down the Sacramento and San Joaquin valleys, bus from Merced depositing me at Yosemite Valley's Curry Village, then picked up by the Tuolumne Meadow Hiker Shuttle the next morning, up to the high country, and deposited at the May Lake trailhead for my hike into a series of High Sierra Camps, light pack on my back and walking sticks in hand.
I saw another monarch butterfly last week, and it set me thinking about some of the incredible things non-human animals do, and what it shows about the place of humans in the cosmos.