1992-08-24 Assigned to PHYSICAL OPTICS CORPORATION reassignment PHYSICAL OPTICS CORPORATION ASSIGNMENT OF ASSIGNORS INTEREST. Assignors: RICH, CHRISTOPHER C.
1992-08-24 Assigned to PHYSICAL OPTICS CORPORATION reassignment PHYSICAL OPTICS CORPORATION ASSIGNMENT OF ASSIGNORS INTEREST. Assignors: AYE, TIN M., HIRSH, JAY W., JANNSON, TOMASZ P.
A high finesse holographic Fabry-Perot etalon and method of making a high finesse holographic Fabry-Perot etalon is disclosed. Particularly, a holographic Fabry-Perot etalon which achieves high finesse despite non-flat interfaces between the etalon media is presented. In a preferred method of fabricating a high finesse Fabry-Perot etalon, single step recording of both holograms simultaneously, with the spacer and substrates in place, is employed which preserves full phase synchronization between the holograms. In spite of imperfections or irregularities of the interface surfaces of the substrates or spacers, the holographic fringes in the holograms remain flat even for slightly different refractive indices between the various media. The position and flatness of the fringes remains similar to perfect Fabry-Perot etalon structure.
This invention pertains to Fabry-Perot etalons. More particularly, this invention relates to holographic Fabry-Perot etalons and a method for making high finesse Fabry-Perot etalons.
The following important relationship defines the influence of spacer flatness on etalon finesse F. ##EQU14## where σl is root mean square (RMS) of spacer flatness. If Equation 14 is satisfied, then the fundamental parameter defining etalon finesse is the reflection coefficient R, and Equation 5 holds. Otherwise, the fundamental parameter determining etalon finesse is surface flatness determined by RMS σl. It is useful to replace the RMS parameter by ##EQU15## where N defines the fraction of a wavelength characterizing surface flatness. For example, for λ=1μ and N=10, the surface flatness RMS is 0.1μ which is a typical flatness for good optical quality surfaces. Using Equation 15, Equation 14 can be transformed into: ##EQU16## This equation is illustrated in Table 2.
It is seen from this table that even obtaining moderate finesse etalons requires interfaces having very high surface flatness, greatly exceeding typical high optical quality surfaces. For example, in order to obtain a moderate finesse etalon of F=61, N must be 378. That is, the surface roughness must only be 1/378 of the wavelength λ, which for λ=500 nm is on the order of a nanometer. This extremely high smoothness obviously cannot be obtained by known low-cost polishing techniques. It would be highly beneficial to have a method of manufacturing high finesse etalons using only moderately smooth interfaces on the order of N =10.
A preferred method of producing a high finesse Fabry-Perot etalon involves providing a reference mirror having a high optical quality surface on the order of λ/100 for recording; providing internal interfaces on the spacer and substrates of moderate optical quality on the order of λ/10; providing a holographic material the recorded structure of which does not change during processing, and employing a single step holographic recording of both holograms simultaneously after assembly of the substrate, spacer, and coating of the holographic material.
7. Removing the reference mirror.
8. Processing the holograms if necessary.
6. Recording the integrated elements by a single step holographic process.
The Fabry-Perot etalon of the present invention may be made tunable by using as the spacer liquid crystal, PLZT, piezoelectric material, or other voltage responsive materials. In such tunable etalons, the etalon transmission characteristic is shifted according to voltage.
Curved Fabry-Perot etalons of high finesse are also made possible by the process disclosed. In one preferred recording arrangement, a curved mirror is used for recording flat holographic plates with slanted structures. In a second preferred set up for recording a curved Fabry-Perot etalon, a curved mirror is used for recording as well as curved holographic mirrors in which holographic fringes are recorded parallel to the surface of the hologram and the curvature of the mirror. Finally, a Fabry-Perot etalon recording set up using phase conjugate mirrors to reverse the wavefront during reflection to insure flatness of the wavefront despite non-uniformity inside the etalon structure is disclosed. Lastly, a spatial light modulator comprising an array of tunable holographic Fabry-Perot etalons of the present invention which are driven by a multi-pixel voltage driving electronic system standard in the art is disclosed.
FIG. 24 is a cross-sectional schematic of a spatial light modulator comprising an array of tunable Fabry-Perot etalons of the present invention.
In accordance with the method of the present invention of producing high finesse Fabry-Perot etalons, a drastically different approach than methods known previously is used. In conventional methods, using either metallic mirrors or interference multi-layers, the mirror structures are evaporated on both sides of the spacer, and the smoothness of the mirror structure naturally follows the smoothness (or roughness) of the spacer. Therefore, it is very difficult to obtain high finesse etalons using conventional methods since flatness is required and determined by large N numbers on the order of 100-300.
Another shortcoming of conventional etalons is related to the fact that it is difficult to apply evaporating techniques to very thin spacers on the order of a few micrometers. Even more difficult is to obtain curved mirror structures providing Fabry-Perot etalons with curved mirrors.
The method herein is based on a single step holographic recording of both mirrors simultaneously with the spacer already installed in the system. A preferred holographic recording setup is illustrated in FIG. 2. Due to single step recording of both holograms simultaneously, full phase synchronization is preserved between the two holograms assuming that the properties of the holographic material do not change during holographic processing. As a result, two standing wave structures are recorded as shown in FIG. 3. In FIG. 3 two holographic structures having sinusoidal modulation substructures are recorded with the spacer already between. Therefore, the two structures which reflect the optical beam illustrated in this figure provide constructive interference assuming that read-out conditions are identical to recording conditions.
In order to fully illustrate that the method of fabrication presented herein provides high etalon finesse, we consider the following simple example of a spherical incident wave reflected from a perfect mirror as shown in FIG. 4. It can be seen that the beam reflected from the mirror is equivalent to the spherical wave emitted from the mirror source. The standing wave created by the incident wave and the reflected wave results in interference which is perfectly flat (like the mirror) if close to the mirror.
The above simple illustration shows that the holographic fringes of the hologram close to the mirror are flat in spite of the formation of the incident wavefront. These wavefront formations can be created either by direct non-uniformities in the incident wavefronts or by non-flatness of the interfaces which are located within the wavefront passage.
where the * indicates the complex conjugate.
I=|μ.sup.(i) |.sup.2 +|μ.sup.(r) .sup.2 +2|r.sub.m |cos (2knz+θ)=1+r.sub.m |+2|r.sub.m | cos(2knz+θ) (Eq. 23).
which determines the nodes of the standing wave.
Only one medium was considered above. The above model is now applied to a three media system illustrated in FIG. 6, and recorded using a standing wave recording set up as shown in FIGS. 7A and B, and resulting in holographic fringes as shown in FIGS. 8A and 8B. In FIG. 7A, the first medium represents a first hologram with thickness T1 and average refractive index n1, the second medium represents a spacer with thickness l and average refractive index ns, and the third medium represents the second hologram with thickness T2 and average refractive index n2. Each of the media has a grating period Λ1, Λ2, and Λs which are the spatial periods of the standing wave structure following the exposure distribution E(z). The above standing wave structure, as shown in FIG. 7B, will be recorded in the form of holographic fringes as shown in FIGS. 8A and 8B with grating periods Λ1, θ2 identical to those in FIG. 7A.
Until now we have considered a Fabry-Perot etalon with perfectly flat interfaces. Assuming slightly varying non-flatness of the interfaces, we can consider the interfaces to be locally parallel. Therefore, we can use the above model for non-flat interfaces.
and it is assumed the thickness of each medium is changed by a factor Δ as follows: ##EQU21## yet total thickness of the system is preserved as before.
and therefore full compensation for the position of the fringes is still achieved. In other words, the position of the fringes does not change in spite of the change in the thickness of each of the medium.
n.sub.1 =n.sub.2 ≠n.sub.s                            (Eq. 33).
As a result of Equation 35 it is seen that if Δ<<N then Δφmax <<2π. This means that even if the thickness of any of the media changes, but Δn<<N, the location of the fringes remains constant. Thus, fringe stability is very high.
It is seen that contrary to Equation 38, only one component of the product is small assuming α1 <<1. Still, Δα remains small. Therefore, the holographic fringes remain flat in spite of refraction on the non-flat interface. The next effect to be considered is the change of grating period Λ with fringe slant. In this case, the period of the slanted wave is ##EQU28## where the slant for normal incidence is ##EQU29## Therefore, the relative change of grating constant is described by ##EQU30## and the typical α1 angle is ##EQU31## Therefore, for typical (moderate) optical quality flatness of λ/10 for Δl=1 cm, we obtain α1 =10-5 =α2. Therefore, the relative change of the grating constant is very small, and is on the order of 10-10. Thus, the following model of the holographic fringes can be considered as correct as shown in FIG. 11.
Therefore, we consider the maximum thickness changes of the media to be on the order of λ for 10 cm holographic etalon plates. Such non-flatness for a conventional Fabry-Perot etalons would completely destroy the fringe structure, while it is quite acceptable for the holographic Fabry-Perot etalon of the present invention as illustrated in the following figures.
All of the above calculations show that despite non-flatness of the internal interfaces, the position and flatness of the fringes remains very similar to a perfect Fabry-Perot etalon structure while only the number of fringes changes.
FIGS. 12A and B compare the interface structures for two types of Fabry-Perot etalons. FIG. 12A is a conventional Fabry-Perot etalon having multilayer mirrors and FIG. 12B is a holographic Fabry-Perot etalon having holographic mirrors. In the first case, interference fringes follow the non-flatness of the interfaces while in the second case the holographic fringes remain flat.
The above-analysis provides the necessary tools to make an optimum Fabry-Perot etalon structure. In order to obtain nearly flat holographic fringes, and as a consequence high etalon finesse, we need to satisfy the following general conditions.
1. The mirror and front surface should be of high optical quality, on the order of N=100.
2. The flatness of the internal interfaces should be of ordinary optical quality on the order of N=10.
3. The holographic material used for recording the etalon holographic mirrors should have processing characteristics such that processing does not change the recording structure, i.e., processing does not change the grating periods Λ1 and Λ2 which were created during recording. A good example of such a material is DuPont photopolymer which requires no wet processing and where development is achieved by UV light. Also, DCG (dichromated gelatin) remains acceptable if all processing steps are very smooth in the sense that the water/alcohol bath conditions are continuously modified during the multi-step bathing processing operation. The temperature of the water and alcohol and the ratio of alcohol to water should not be drastically changed between adjacent processing baths. Such procedures can provide high etalon finesse, on the order of more than 100, even for large etalon plates with sizes larger than 10 cm.
In the case of DCG, the tradeoff between obtaining high reflectivity holographic mirrors, which is a necessary condition for high finesse, and providing sufficient conditions to obtain smooth processing must be considered. Significant changes in the refractive index during processing, higher than 0.01, and possible deformation of holographic material non-uniformity must be avoided.
The above-discussed conditions may be fulfilled using the following fabrication steps to produce a Fabry-Perot etalon of the present invention as shown in FIG. 13. Step 1 is to provide a flat (substrate) having a highly flat "front surface" on the order of λ/100, shown as "Flat 2" in FIGS. 13 and 14. The "interface" of Flat 2 (adjacent hologram 2) can be of moderate optical quality on the order of λ/10. A holographic coating is made on the interface of Flat 2 as shown in FIG. 14.
Step 2 involves providing a flat, "Flat 1", having a back surface and interface of a moderate optical quality on the order of λ/10, shown as "Flat 1" in FIGS. 13 and 15. A holographic coating is made on the interface of Flat 1 as shown in FIG. 15.
Step 3 is to provide a mirror having high optical quality on the order of λ/100.
Step 4 is to provide a spacer having moderate flatness on the order of λ/10.
Step 5 is to integrate all four elements (Hologram 1-Flat 1, Hologram 2-Flat 2, Mirror, and Spacer) by providing a matching layer between each element according to FIG. 13. The matching medium may be an adhesive made for this type of use such as that made by Norland. All refractive indices should be only slightly different with no difference greater than 0.01.
Step 6 is to provide a single step holographic recording using the geometry as shown in FIG. 7A above.
Step 7 is to remove the mirror.
Step 8 is to process the holograms if necessary.
A second procedure which may be followed to satisfy the conditions for flat holographic fringes despite non-flat interfaces and to produce an etalon as depicted in FIG. 16 is now described. Step 1 is to provide a spacer having moderate optical quality on the order of λ/10.
Step 2 is to provide a holographic coating on both sides of the spacer.
Step 3 is to provide a flat having high optical quality on the order of λ/100 on the front surface and having moderate optical quality on the order of λ/10 on the interface.
Step 4 is to provide a mirror having an optical quality of λ/100.
Step 5 is to integrate the components using a matching medium as before.
Step 6 is to provide a single step holographic recording.
The resulting Fabry-Perot etalon is shown in FIG. 16. The spacer can be of a number of different types, depending on the type of etalon performance desired, either stationary or tunable, or whether a high or low spacer thickness is needed. The typical spacer for very low spacer thickness, on the order of a few microns, is a plastic such as Mylar. Unfortunately, Mylar is highly anisotropic and therefore a glassy material is more preferable. The glassy material may be evaporated on the substrate.
Other types of spacers can simply be free space. It should be emphasized that this new type of Fabry-Perot etalon provides the possibility of using very thin spacers contrary to conventional etalon systems where the evaporating process requires using thick spacers for stability reasons.
In the case of tunable Fabry-Perot etalons, the types of spacers that can be used include liquid crystal (LC) with two metallic electrodes evaporated on both sides of the LC or evaporated on the substrates adjacent to the LC. PLZT, piezoelectric, or others types of spacers may be used. In the case of holographic recording of a tunable system, recording may preferably be accomplished after integration of all elements.
A tunable Fabry-Perot etalon is shown in FIG. 17 having metal electrodes sandwiching an electrooptic material. On either side of the sandwich is a flat-hologram subcombination. The refractive index of the EO material constituting the spacer changes according to voltage. Therefore, the etalon transmission characteristic is shifted according to voltage and changes as shown in FIG. 18.
Curved Fabry-Perot etalons are also made possible by the novel process of this invention. In contradistinction to the above approaches, curved mirrors are used for recording. During recording, the holographic etalon structure can be separated from the mirror as illustrated in FIGS. 19 and 20. In FIG. 19, the holographic mirrors are flat and slanted structures are recorded in the flat hologram. In FIG. 20, the curvature of the hologram follows the curvature of the recording mirror, and the holographic fringes are, therefore, parallel to the surface of the hologram and follow the curvature of the recording mirror. In FIG. 21 a Lippmann holographic structure recorded using the set up shown in FIG. 20 is illustrated. FIG. 22A illustrates a three dimensional holographic recording structure which may be used to record slanted fringes using a curved mirror as previously depicted schematically in FIG. 19. FIG. 22B shows the recorded slanted fringes.
In order to obtain a good quality reflected wavefront for a Fabry-Perot etalon, it may be preferable to use phase conjugate mirrors for holographic recording as shown in FIG. 23. A phase conjugate mirror operates to reverse the wavefront during reflection. In such a case, the perfectly plane incident wavefront will be exactly reversed. So in spite of wavefront non-uniformity inside the etalon structure, the wavefront remains flat.
A spatial light modulator (SLM) structure is illustrated in FIG. 24 based on an array of tunable holographic Fabry-Perot etalons of the type shown in FIG. 17. In such a case, each SLM pixel comprises a Fabry-Perot etalon which may be independently driven by a multi-pixel voltage driving electronic system standard in the art. Such a system can be provided by using typical high definition TV large display fabrication procedures.
It is to be understood that embodiments of the present invention not disclosed herein are fully intended to be within the scope of the claims.
2. The invention as defined in claim 1 further characterized in that the coating is a photopolymer.
3. The invention as defined in claim 1 further characterized in that the coating is a dichromated gelatin.
4. The invention as defined in claim 1 wherein the spacer is an electrooptic material.
5. The invention as defined in claim 1 wherein the spacer is air.
6. The invention as defined in claim 1 wherein the spacer is liquid crystal.
7. The invention as defined in claim 1 wherein the spacer is PbLa(TiZr)O3.
8. The invention as defined in claim 1 wherein the spacer is a piezoelectric material.
9. The invention as defined in claim 1 wherein the spacer is a material the refractive index of which is affected by light.
11. The invention as defined in claim 2 further characterized in that the holographic material is a photopolymer.
12. The invention as defined in claim 2 further characterized in that the holographic material is dichromated gelatin.
13. The invention as defined in claim 2 wherein the spacer is an electrooptic material.
14. The invention as defined in claim 10 wherein the spacer is liquid crystal.
15. The invention as defined in claim 10 wherein the spacer is PbLa(TiZr)O3.
16. The invention as defined in claim 10 wherein the spacer is a piezoelectric material.
17. The invention as defined in claim 10 wherein the spacer is a material the refractive index of which is affected by light.
recording the holographic material using a single step holographic recording process.
a phase conjugate mirror adjacent the holographic material of the second side.
multi-pixel voltage driving means for driving each tunable Fabry-Perot etalon independently of the other etalons.
"Multiplexed Holographic Fabry-Perot Etalons", Lin et al., Applied Optics, vol. 31, No. 14, May 10, 1992 (pp. 2478-2484).
C. P. Kuo, T. Aye, D. G. Pelka, J. Jannson, and T. Jannson, "Tunable holographic Fabry-Perot etalon fabricated from poor quality-glass substrates," Optics Letters, vol. 15, No. 7, Apr. 1, 1990, 351-353.


text:
Press Releases /
Preview A+A 2017
This article is available in the following languages:
World's No. 1 Trade Fair for Safety, Security and Health at Work as big as ever: 70,000 m² rented out to over 1,900 exhibitors
A+A 2017 as big as ever: 70,000 m² rented out to over 1,900 exhibitorn (c) Messe Düsseldorf GmbH / ctillmann
Every 15 seconds a worker dies as a result of occupational diseases or accidents according to estimates of the International Labour Organisation (ILO). Therefore it must be one of the highest priorities for every company to maintain and update occupational safety standards. This is where A+A 2017 comes in as the leading international trade fair and congress for safe and healthy working. Under the heading "People Matter" it will present everything related to safety, security and health at work from 17 to 20 October. This year the ranges from the (for the first time) 1,900 exhibitors from 63 nations are so wide that A+A will occupy over 70,000 squares metres of exhibition space at the Düsseldorf exhibition centre for the first time in its history.
Our world of work has changed in many ways and increasingly calls for adjustments to occupational safety. Higher and increasing workloads and a growing number of jobs requiring multi-tasking are all consequences of digitalisation – and these consequences are now decisively driving change in our world of work impacting nearly all workplaces. However, demographic change also brings new challenges and opportunities. Commenting on this Joachim Schäfer, Managing Director at Messe Düsseldorf, said: "Accordingly, all measures undertaken to preserve the ability to work are just as important as safety and security proper at the workplace because these improve people's lives by also protecting them against health and safety risks at their workplaces. At the same time, these measures increase productivity and, hence, the competitiveness of companies."
World's No. 1 Trade Fair Set to Break Exhibition Space and Exhibitor Records
A+A – the world's leading Trade Fair for Safety, Security and Health at Work – and the 35th International Congress for Occupational Health and Occupational Medicine held in Düsseldorf from 17 to 20 October will show what these measures could look like. Both events provide a complete overview of the latest trends and products worldwide in the areas of occupational safety, corporate health promotion and security management at companies. For the first time in the history of A+A more than 1,900 exhibitors from 63 countries will be occupying over 70,000 square metres in nine exhibition halls where they will showcase their latest products and services for personal protection and the implementation of health-maintaining, safe operations. Exhibits range from corporate fashion and ergonomic office furniture through personal protective equipment to fire protection and emergency management as well as corporate environmental protection measures. A+A is the most important event for all experts from occupational health and safety management, for HR managers and works council members, industry buyers, specialist retailers, company physicians, fire brigades, technical relief and law enforcement officers, representatives of employers' liability insurance associations and accident insurance firms as well as the owners of small and medium-sized enterprises.
A+A Congress: The Most Important Congress Event for the Sector
Held in parallel with the A+A trade fair, the 35th International Congress for Occupational Safety and Occupational Medicine will provide comprehensive information on the current issues and challenges facing the sector. The congress has been organised by Basi – the German Federal Association for Occupational Safety and Health – since the early 1950s. Lined up are in excess of 50 lecture series that address current issues and flag up solutions to these problems. Once again the conference of ILO – the International Labour Organisation – will form a globally respected part of the A+A Congress programme. Here high-calibre labour, safety and health experts will address such topics as "Violence and Psychosocial Risks at Work", "Safety and Health in Global Supply Chains", and "Capture and Use of Data on Safety and Health – How Companies and Employees can Benefit".
New: A+A Highlight Route
The special focus of A+A 2017 will be the "Future of Work" – a theme impressively staged on the new A+A Highlight Route. Across all halls 12 exhibitors such as BORNACK, Honeywell, Uvex and IFA, the Institute for Occupational Safety of German Statutory Accident Insurance, will showcase highlights related to "Smart PPE", "Digitalisation of Work" and "Digital Applications and Solutions" – ranging from smart respiratory and skin protection programmes through back-saving exoskeletons and medical wearables to intelligent fleet management, data glasses and sensor-controlled fall protection. With this new concept A+A provides a stage for digitalisation – the future topic that is already a given in many areas of life, let alone work. "Employees are faced with ever more complex challenges that call for a higher degree of flexibility and mobility – and with more monitoring and control," says Birgit Horn, Director A+A, quoting representative studies. The Germany-wide survey "DGB-Index Gute Arbeit 2016" (German Trade Union Congress Index for Decent Work 2016) found that 82% of employees are influenced by digitalisation processes in their work – 60% of them to a high or very high degree.
As Topical as Ever: Fire Prevention
Connected data will in future also be indispensable for fire prevention and protection – from drawing up hazard prevention plans for response preparation and the simulation of relief operations for training purposes to actual rescue operations on site. This is why one of the stops on the A+A Highlight Route is the established Theme Park Industrial Fire Protection and Emergency Management in Hall 6, where digital fire extinguishers will be presented for training purposes, to name but one exhibit. Furthermore, informative presentations and live demonstrations will show the measures and concepts that can help prevent accidents, large-scale incidents and the need for rescue operations. The Düsseldorf fire brigade academy will demonstrate live on the outdoor premises how firemen are trained in realistic settings. As the most important sectoral platform for personal protective equipment worldwide A+A 2017 will also present all innovations in the field of protective gear for firefighters.
A+A live: Experience Safe and Healthy Work with all the Senses
More examples of best practice using state-of-the-art products and processes will be shared under the heading "A+A live" at forums, Theme Parks and special shows. As is the case with the spectacular special show Safe Rescue from Highs and Lows organised by the THW in cooperation with the DLRG in Hall 6.
In Hall 10 trade visitors will find the Meeting Point Safety and Health as a centre of expertise for questions related to safety and health at work. The neighbouring stage programme Workplace Design & Corporate Health focuses on the ergonomic design of workplaces and processes in offices as well as corporate health promotion.
In Hall 11 at the Trend Forum Safety & Security simple and easy-to-grasp talks on "Explosion Protection", "Safe Handling and Storage of Hazardous Substances", "Industrial Fire Protection and Emergency Management" as well as "Fall Protection" will provide insights into current developments. Also located in Hall 11, the dynamic, re-vamped A+A Fashion Shows staged several times daily will show how fashionable and diverse modern workwear and protective clothing is today. After all: top design and safety are no longer a contradiction in terms.
Partner Country Great Britain
The line-up of side events for A+A 2017 is rounded off by the activities related to the partner country Great Britain. These are aimed at establishing an Anglo-German OSH dialogue involving important industry associations, institutions and political protagonists. Britain's Health and Safety Executive (HSE), an independent body of experts advising the British Government, will play a part in the trade fair and the special shows [...]as well as deliver talks at the Congress and the ILO Conference. The HSE acts in the public interest with the aim of minimising fatal accidents at work and serious work-related diseases in the British working environment.
The partner country was chosen by the advisory board for the event as early as at A+A 2015, i.e. well ahead of the Brexit referendum, but in view of the altered conditions cross-border exchange of experience is becoming even more important. The current political situation also raises many questions for the suppliers of protective items and safety equipment. As the decisive industry platform A+A 2017 will provide scope for an in-depth discussion on commercial and institutional relations and an opportunity to learn more about the British market with its just under 32 million gainfully employed.
Exhibitor attendance from Great Britain has traditionally been among the highest at A+A: 2017 sees 82 exhibitors displaying innovative products and services on more than 2,900 square metres.
For current information on A+A 2017 and the International Congress go to www.aplusa.de.
A+A 2017 will be held from 17 to 20 October and is open daily from 9.00 am to 6.00 pm.
We would appreciate a sample copy of any reprints.
PDF Press Release: Preview A+A 2017
JPG Photo: A+A 2017 as big as ever: 70,000 m² rented out to over 1,900 exhibitor (c) Messe Düsseldorf GmbH / ctillmannn

redpajama_set_name: RedPajamaCommonCrawl


Fields Medal (1966) for his work in differential topology where he proved the generalized Poincaré conjecture in dimension n>=5.
Stephen Smale's hometown Flint is renowned as the former production site of the U.S.'s largest car company General Motors. Smale's father worked for GM and from the age of five Smale lived on a farm outside the city. The country elementary school where he spent eight years had just one teacher. Smale's favourite subjects were chemistry and physics. As a student at the University of Michigan, it was after he first failed a Physics course that he turned to Mathematics (taking his Bachelor degree in 1952 and his Masters in 1953). Smale received his Ph.D. at the University of Michigan, Ann Arbor in 1957 and from 1956-58 worked as a lecturer at the University of Chicago. With the help of a postdoctoral fellowship from the National Science Foundation, he spent 1958-60 at the Institute for Advanced Study in Princeton and the Instituto de Mathematica Pura e Aplicada in Rio de Janeiro. In 1960, Smale was appointed assistant professor at the University of California, Berkeley. In 1961 he accepted an appointment at Columbia University in New York but returned to Berkeley in 1964. Since he retired from Berkeley in 1995, Smale has also been a professor at the City University of Hong Kong.
Smale was awarded the Veblen Prize for Geometry by the American Mathematical Society (1966). He has received the U.S. National Medal of Science (1996) and other awards including the Chauvenet Prize of the Mathematical Association of America ( 1988), the Von Neuman Award (1989), and the Jürgen Moser Prize (2005) from the Society for Industrial and Applied Mathematics. Smale holds seven honorary doctorates and is honorary member of the Instituto de Mathematica Pura e Aplicada Rio de Janeiro (since 1990), the Trinity Mathematical Society in Dublin (since 1991), the Moscow Mathematical Society (since 1997) and the London Mathematical Society (since 1998).
Stephen Smale is famous for his work in dynamical systems and the invention of so-called horseshoe mapping. This method allowed him not only to solve problems from chaos theory, but also one of the great classic problems of topology, the generalized Poincaré conjecture for dimension 5 and higher. It says that every compact connected n-manifold, on which a circle can be contracted to a point, is homeomorphic to the surface of a sphere in dimension n+1 – that is, this manifold can be transformed without cutting or gluing into a spherical surface. Poincaré had formulated this conjecture for dimension 3; Smale was at able to show the generalized conjecture for dimension 5 and higher.
Later, Smale produced further significant results in the field of dynamical systems, topology, and in the calculus of variations, before turning to economics in the 1970s. There he formulated an economic equilibrium condition using methods from dynamical systems. This work led him later to the field of numerical analysis and complexity theory.
Stephen Smale is not only known for his mathematical achievements, but also for the world-class collection of minerals that he and his wife have over decades built up.


text:
Q: AWS Cognito - Custom email message with Lambda trigger being overwritten I'm using a lambda function to customize confirmation emails with AWS Cognito. My lambda function seems to work fine and looks like this:
exports.handler = async (event, context, callback) => {
  const sampleTemplate = `

${event.request.codeParameter}

${event.userName}

  `

  if (event.triggerSource === "CustomMessage_AdminCreateUser") {
    event.response.emailSubject = 'Lets hope this works'
    event.response.emailMessage = sampleTemplate

    console.log(event.response) // Logs look as expected
  }

  callback(null, event);
};

The problem is that when the emails arrive the message body is being overwritten by the content in the User Pools > Message Customizations tab. The subject line is working fine, but the email body is being overwritten. For example, the cognito settings look like this:

And the emails look like this:

As you can see, the lambda function worked for setting the email's subject line, but not the actual content. I can't find any setting to turn off that content and it can't be left blank... Any help is much appreciated.

A: For anyone finding this, I was able to find the answer. When using the CustomMessage_AdminCreateUser event, cognito will silently throw an error if you use event.userName in the template. Instead use event.request.usernameParameter and it will work

A: If after doing everything, your custom email template doesn't show up then check the following:

*

*Verification type is set to "code" not "link". ( Your Pool > General settings > message customizations ) Ref: https://github.com/amazon-archives/amazon-cognito-identity-js/issues/521#issuecomment-358383440

*Email HTML template shouldn't exceed more than 20,000 UTF characters. Ref: https://docs.aws.amazon.com/cognito/latest/developerguide/user-pool-lambda-custom-message.html#aws-lambda-triggers-custom-message-example

*Check this tutorial - https://medium.com/@hasnat_33856/customize-your-cognito-verification-emails-with-html-pages-using-lambda-function-e6fff7ebfb94

A: We MUST include both the "{username}" and "{####}" placeholder for the custom template for CustomMessage_AdminCreateUser to work. We can place this ourselves in the html file or via the event object's values for the keys event.request.usernameParameter and event.request.codeParameter respectively.
In summary, the html file for CustomMessage_AdminCreateUser must include these two values:
event.request.usernameParameter (has value "{username}") and
event.request.codeParameter (has value "{####}")

redpajama_set_name: RedPajamaStackExchange


text:
A letter to fans from 49ers CEO Jed York
Dec 30, 2014 at 8:34 AM • --
San Francisco 49ers CEO Jed York sent a letter via email to season tickets holders last night. It read as follows:
I would like to take this opportunity to speak directly to you, our Faithful fans.
After spending two years constructing a new home for you and our team, the 2014 season began with great anticipation and high hopes. On the field, we looked to build on three consecutive years of success and take that last step toward achieving our ultimate goal. Unfortunately, we were unable to capitalize and accomplish our objective.
As the CEO of this team, it is my responsibility to ensure we are always on the path to success. Yesterday, a change was made that I believe is in the best interest of this team. Change is often accompanied by skepticism, and I respect your right to have questions. Ultimately, the decisions we make as an organization will be judged by their results, and the best way to answer concerns is by putting a championship product on the field.
The 49ers experienced a period of success under Jim Harbaugh's direction that we will look back on proudly, and for that we owe him our gratitude. The reality we now face is that the time has come for this team to move in a different direction – one that gets us back on the path to realizing our goals.
Now, our focus is squarely concentrated on solidifying the future of this team and finding our next head coach. Having successfully navigated this process in the past, Trent Baalke has my full confidence in leading our coaching search. We have an exciting opportunity ahead of us and look forward to adding more talented individuals to this organization.
As we move into the next chapter of our team's history, I think back to an earlier time. In 1977, my grandfather brought our family to the 49ers and began to create a championship standard. That standard is now my responsibility to uphold and our efforts will be completely dedicated to that cause.
I share and respect your passion for this team because I was born with it. You are the most Faithful fans in the National Football League and you deserve a team that makes you proud.
Jed York
49ers fans show up in droves to make road win over Rams feel like a home game
By Kirk Larrabee
The 49ers may have technically been on the road Sunday in their regular season finale against the Los Angeles Rams, but enough of their fans showed up to make SoFi Stadium in Inglewood feel like home for the visiting team. 49ers fans made their presence felt as they watched their team rally from a 17-point first half deficit to snag a memorable 27-24 overtime win over the Rams, sealing a playoff berth in the process. Multiple 49ers players commented afterwards that the fan presence made the game feel like a home contest. "It definitely did," wide receiver Deebo Samuel said. "I feel like the Rams pumped noise because there wasn't that many Rams fans in here." Linebacker Fred Warner said that one of the officials told him how impressive it was to see
'They'll be a real, real mess to deal with': Cowboys' Jerry Jones offers scouting report on 49ers, has no concerns over opposing fans
While the San Francisco 49ers are preparing to head on the road for the start of the playoffs, the Dallas Cowboys are preparing to host Kyle Shanahan's squad. Naturally, the last thing the Cowboys want to see is a takeover of their home stadium, which is what we saw at SoFi Stadium during the regular-season finale against the Los Angeles Rams. On Tuesday morning, Cowboys owner Jerry Jones joined 105.3 The Fan and acknowledged that he has no control over who buys the tickets. However, he boasted about the Cowboys having the highest resale ticket prices in the NFL right now, which he feels could help limit the number of opposing fans for the playoff matchup. Although, he also
Watch: 49ers, Cowboys fans stampede into AT&T Stadium
Jon Machota of The Athletic posted the following video of fans stampeding into AT&T Stadium when doors opened for the Wild Card playoff game between the San Francisco 49ers and Dallas Cowboys two hours before kickoff. AT&T Stadium doors have opened for Cowboys vs. 49ers pic.twitter.com/OtewlvaL82— Jon Machota (@jonmachota) January 16, 2022 Why


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Davis: Everyone Just Calm Down
By NUHighlights Apr 4, 2014, 2:51pm CDT
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SO YOUR FOOTBALL TEAM IS TRYING TO UNIONIZE
Look, I get it. Unions are polarizing and we may be facing a significant change to something that we love. This does not mean that we need to start pounding our fists and harrumphing until our opinion is heard in Evanston. Let me take you through a handful of fan-specific issues that seem to be getting a lot of attention.
You know what, I'm not even going to touch this one. We all know that this is not about getting a salary.
DIFFERENT OPINIONS
Let's stop treating all players and all previously recognized employees of Northwestern as if they share one of two opinions. Each player feels differently. Each member of that athletic department feels differently. They hold personal and professional opinions. We can't assume future legal action or a willingness to negotiate just based on the current appeal. We also can't assume that President Shapiro, Dr. Phillips, Pat Fitzgerald and on down the line are vehemently opposed to unionization. They are probably quite conflicted. They likely want changes to be made and may even have doubts as to whether the NCAA can get those done.
And don't forget that this is brand new for them, as well. They may fear the unintended consequences. They don't want to see people lose their jobs within athletic departments or programs get cut because of something that might come from this. That's certainly not to say that such things will happen, but we don't know. These are reasonable fears of an unknowable future.
BURNED BRIDGES
None of us want to see damaged relationships between Kain Colter and the program. This also isn't really our business. Everyone involved is an adult and I'm sure these relationships will change over time. Whatever is going on inside the university or between the university and former players could very well blow over in time. It also shouldn't impact the far more serious issues being discussed within the unionization effort. Let them figure that out.
There has not been any indication that this is a distraction to the team, somehow making the on-field product worse. The locker room distraction has been a favorite point of conjecture for columnists and fans for decades. It's also often completely bogus. This is not a particularly time-consuming issue for them. And, to the best of my knowledge, the locker room has not divided into two halves with semi-regular West Side Story-inspired melees. You know what is a distraction to their football success? Having to go to class, study, and write papers. But that's what they agreed to do when they signed the scholarship agreement and so far they've balanced that pretty well.
Also, video games. Lots of video games. I'm onto you, guys.
WE'RE GOING TO BE FINE
A lot of great points were made on this week's West Lot Pirates podcast, specifically that it's okay that we don't know all of the ramifications of a potential union. Yet, those questions should not be a deterrent to trying to improve a flawed system. We all love college sports and most of us hate change. I'm one of those people. College sports fans are some of the most conservative, tradition-based fans in sports. We've been agitated by significant conference realignment over the past few years. But guess what: we'll still have college sports. It may be different, but hopefully improved. We'll still get to be irrational fans yelling at the TV. It's not going away.
THIS ISN'T ABOUT US
It's about the players. They are the ones who put in the time and sacrifice their bodies, not for our amusement, but for scholarship-based compensation. An idea has been floated by some fans that we should be trying to influence members of the Northwestern football team leading up to their vote on April 25. Most of us on both sides will agree that is lunacy, but it points to a larger trend that somehow our political opinions are relevant in this. They are not. Whether you are for unions, against them, or have no opinion, this is up to the players. It is their lives, not just the four or five years in college, but for the decades that follow.
Of course, there are also selfish reasons to care about the well-being of the athletes. Given the significant media attention that concussions and other health concerns have received by the national media, we run the risk of facing a shrinking pool of talent. Last fall, Outside the Lines reported that youth football participation had fallen by 9.5% between 2010 and 2012, the largest two-year decline for Pop Warner in their history. As information about potential medical concerns spreads to parents and young athletes, we may see more people turning away from football. If high school athletes start to fear an absence of long-term medical coverage from injuries suffered in college, the effect on college football could be significant: less talent, declining parity, and a less enjoyable "product" for fans to watch.
CAPA would have its biggest impact on future generations of college athletes if a union comes to fruition. The football team will vote based on a balance of their own immediate interests, those of others around the country who have worse medical coverage and only single-year guarantees on scholarships, and those of future athletes not yet born. There will likely be unintended consequences. They are facing an unknown, something completely new to the world of college athletics. This isn't an easy decision to make, so let's respect their privacy and their intelligence by leaving them alone.
A look into the career of Ryan Smith, Northwestern's new cornerbacks coach The Sky Team has a new co-pilot.


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Fired Hillsong Pastor Carl Lentz Denies Former Nanny's Sexual Abuse Claims
"I was physically violated by his unwanted and repeated sexual touching of my intimate areas. I froze. Every time, I froze," Leona Kimes alleged of Carl Lentz, who she previously worked for.
By Alyssa Morin Jun 02, 2021 12:40 AMTags
LegalControversyReligionCelebritiesSexual Assault
Watch: Pastor Carl Lentz Admits to Infidelity After Hillsong Church Firing
Seven months after Carl Lentz was fired from the megachurch Hillsong, new allegations about him have come to light.
Hillsong Church Boston co-pastor Leona Kimes, who previously worked as a nanny for the disgraced pastor and his family, claims she was "subjected to manipulation, control, bullying, abuse of power, and sexual abuse" in Lentz's home over the course of seven years.
On Monday, May 31, Kimes published an essay titled "Writing My Voice Back" on Medium, in which she made accusations against the former Hillsong pastor. Although Kimes didn't identify Lentz by name in her story, she confirmed her accusations were about him in a statement to Religion News Service.
"I felt trapped and silenced. I also felt so ashamed and I had been told not to say anything or tell anyone," she told the outlet.
Following Kimes' claims, a legal rep for Carl and his wife, Laura Lentz, told Religion News Service they both "vehemently deny the allegations and, in addition to that, have irrefutable proof the events did not happen as they are being described."
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E! News has reached out to the couple's rep and attorney for comment. However, we have yet to receive a response.
In her essay, Kimes described her work environment with Lentz and his family before she moved to Boston, where she now serves as a pastor alongside her husband. While working as a nanny for the family for seven years, Kimes explained that she not only took care of Lentz's kids, but she cleaned their house, as well as ran errands for them.
Toby Zerna/Newspix/Getty Images
While Kimes explained "there were joyful moments," she also claimed that she "experienced a great deal of pain."
As she put it, "The boundaries between personal and professional blurred early on, and an unhealthy bond and attachment was formed."
Kimes alleged the "sexual abuse started small," noting that Lentz would make comments about her appearance. "My pastor would look at me and say, 'Gurl, you're looking good. You've been in the gym?'" she claimed. "There was a lot of flirty teasing like this."
Charley Gallay/Getty Images
Additionally, Kimes accused the former pastor of "crossing more boundaries."
"When I was sitting in the hot tub with the kids, he would get in, positioning himself close to me so his hands could graze my legs," she recalled of one incident.
"Then the physical encounters escalated," she explained. "While he never had intercourse with me and never kissed me, I was physically violated by his unwanted and repeated sexual touching of my intimate areas. I froze. Every time, I froze."
Kimes said Lentz's "inappropriate touching and suggestive text messages were addressed by both lead pastors on two occasions during my time serving in their home." But despite coming forward, Kimes alleged that she was "blamed and silenced" in both instances.
Following Kimes' claims, Hillsong Church founders Brian and Bobbie Houston issued a statement, which read in part, "After the termination of the former Lead Pastor of Hillsong East Coast, it was clear the issues were significant and because of our concerns, we initiated an independent and lengthy investigation into the culture of all four Hillsong East Coast locations."
"In the process of seeking clarity, hearing Leona Kimes' experience was very disturbing," the statement continued. "We have respected Leona's privacy and her deeply personal story. She has now decided to share her experience so that she and her husband can continue moving forward as a family."
The founders said they are "committed to learning more about how to identify such trauma and bring meaningful support to anyone who has experienced it."
Slaven Vlasic/Getty Images
Ultimately, Kimes said she was fired from her nanny role in the summer of 2017 after telling Lentz she was going to find another job.
"I can't forget how he took away my confidence. I can't forget how he took away my voice," she wrote. "I can't forget about the days I laid in bed that year believing that I didn't deserve to be on this earth and entertaining ideas of how to end it all. Unfortunately, I can't forget any of it."
She added, "Even though I can't forget it, I believe I can use it to become stronger. Through intense therapy, I now recognize that it wasn't my fault. I didn't fail. Church didn't fail me. God didn't fail me. Man did."
After being fired from Hillsong, Lentz admitted to infinitely.
In a statement shared on Nov. 5, 2020, he stated, "I was unfaithful in my marriage, the most important relationship in my life and held accountable for that," the pastor stated. "This failure is on me, and me alone and I take full responsibility for my actions."


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Man United legend Nani set for Venezia medical
According to Sky Sport Italia, former Manchester United winger Nani is on the verge of joining Venezia and has already landed in Italy to undergo his medicals with the Lagunari.
The 35-year-old's contract with Orlando City expired at the beginning of the month and both Bologna and Genoa had been offered the chance to sign the former Portugal international.
However, Nani is reportedly close to reaching an agreement with Venezia.
The deal is almost done as, according to the report, Nani has already arrived in town and is expected to undergo his medicals in the coming hours.
Nani scored 31 goals in 87 games in the MLS and is set to return to Italy after a one-year spell at Lazio, where he failed to impress, scoring three goals in 25 appearances in 2017-18 under Simone Inzaghi.
Nani scored 40 goals in 230 games with Manchester United between 2007 and 2014. He won the Champions League and four Premier League titles at Old Trafford.
Venezia, Nani in città per le visite mediche: il sogno di mercato è vicino#SkyCalciomercato #Calciomercato #SkySport #Venezia #Nani https://t.co/8t7a2sUU7B
— skysport (@SkySport) January 14, 2022
ask asjk on Jan 14, 2022 11:28 at 11:28 am
""Legend"… You keep on using this term… I dont it you know what it means to be a legend
Andy on Jan 14, 2022 12:18 at 12:18 pm
Legend? Lol
Dazziano Colucci on Jan 14, 2022 14:26 at 2:26 pm
Yeah the term Legend is just bounded around these days. If Nani is a United Legend, you would be placing him in the same company as Charlton, Giggs, Cantona, Laws etc, etc.
Whatever on Jan 14, 2022 14:30 at 2:30 pm
Is this a troll post? What kind of a legend? 😀
Man, what a career finale, getting to live in Venice at a time of reduced tourism. I'd also be keen to sign for Venezia over Bologna or Genoa.


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Category: Culture
Transactions on BSP-registered foreign portfolio investments for November 2019 yielded net outflows of US$345 million as a result of the US$1.5 billion outflows and US$1.2 billion inflows for the month. This is in contrast from the net inflows noted …
MANILA Department of National Defense (DND) Secretary Delfin Lorenzana has formally recommended to President Rodrigo R. Duterte not to extend martial law in Mindanao once its third extension lapses by yearend.Lorenzana, in a message to reporters, said …
MANILA President Rodrigo Roa Duterte has extended his congratulations to the six recipients of this year's The Outstanding Filipino (TOFIL) Awards as models of excellence through hard work to uplift the economic development of the country.TOFIL 2019 Na…
51 more Filipino veterans get US Congressional Gold Medal Award
MANILA – A total of 51 Filipino World War II veterans posthumously received on Tuesday the prestigious US Congressional Gold Medal Award for their gallantry during the war in defense of freedom and democracy.During the awarding ceremony at the AFP Offi…
Business & Finance, Culture
Andanar condemns NPA bomb attack in E. Samar
MANILA � Presidential Communications Operations Office Secretary Martin Andanar on Friday denounced the recent bomb attack by the Communist Party of the Philippines' (CPP) armed wing, the New People's Army (NPA), in Eastern Samar that killed at least s…
Ramon Tulfo posts bail for 2 libel cases
MANILA Columnist Ramon Tulfo has posted bail for the libel and cyber libel complaints filed against him by Executive Secretary Salvador Medialdea.A Nov. 8 order signed by Manila Regional Trial Court Branch 12 Judge Renato Enciso said Tulfo posted a ca…
Cebu archbishop appointed member of Vatican council for culture
MANILA Pope Francis has appointed Cebu Archbishop Jose Palma as one of the members of the Pontifical Council for Culture.According to an article posted on the Catholic Bishops' Conference of the Philippines (CBCP) news website, the 69-year old Catholi…


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Kolmogorov–Smirnov test
Illustration of the Kolmogorov–Smirnov statistic. Red line is CDF, blue line is an ECDF, and the black arrow is the K–S statistic.
In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test). It is named after Andrey Kolmogorov and Nikolai Smirnov.
The Kolmogorov–Smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution (in the one-sample case) or that the samples are drawn from the same distribution (in the two-sample case). In the one-sample case, the distribution considered under the null hypothesis may be continuous (see Section 2), purely discrete or mixed (see Section 2.2). In the two-sample case (see Section 3), the distribution considered under the null hypothesis is a continuous distribution but is otherwise unrestricted.
The two-sample K–S test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples.
The Kolmogorov–Smirnov test can be modified to serve as a goodness of fit test. In the special case of testing for normality of the distribution, samples are standardized and compared with a standard normal distribution. This is equivalent to setting the mean and variance of the reference distribution equal to the sample estimates, and it is known that using these to define the specific reference distribution changes the null distribution of the test statistic: see below. Various studies have found that, even in this corrected form, the test is less powerful for testing normality than the Shapiro–Wilk test or Anderson–Darling test.[1] However, these other tests have their own disadvantages. For instance the Shapiro–Wilk test is known not to work well in samples with many identical values.
1 Kolmogorov–Smirnov statistic
2 Kolmogorov distribution
2.1 Test with estimated parameters
2.2 Discrete and mixed null distribution
3 Two-sample Kolmogorov–Smirnov test
4 Setting confidence limits for the shape of a distribution function
5 The Kolmogorov–Smirnov statistic in more than one dimension
6 Implementations
Kolmogorov–Smirnov statistic[edit]
The empirical distribution function Fn for n iid ordered observations Xi is defined as
F n ( x ) = 1 n ∑ i = 1 n I [ − ∞ , x ] ( X i ) {\displaystyle F_{n}(x)={1 \over n}\sum _{i=1}^{n}I_{[-\infty ,x]}(X_{i})}
where I [ − ∞ , x ] ( X i ) {\displaystyle I_{[-\infty ,x]}(X_{i})} is the indicator function, equal to 1 if X i ≤ x {\displaystyle X_{i}\leq x} and equal to 0 otherwise.
The Kolmogorov–Smirnov statistic for a given cumulative distribution function F(x) is
D n = sup x | F n ( x ) − F ( x ) | {\displaystyle D_{n}=\sup _{x}|F_{n}(x)-F(x)|}
where supx is the supremum of the set of distances. By the Glivenko–Cantelli theorem, if the sample comes from distribution F(x), then Dn converges to 0 almost surely in the limit when n {\displaystyle n} goes to infinity. Kolmogorov strengthened this result, by effectively providing the rate of this convergence (see below). Donsker's theorem provides yet a stronger result.
In practice, the statistic requires a relatively large number of data points (in comparison to other goodness of fit criteria such as the Anderson–Darling test statistic) to properly reject the null hypothesis.
Kolmogorov distribution[edit]
The Kolmogorov distribution is the distribution of the random variable
K = sup t ∈ [ 0 , 1 ] | B ( t ) | {\displaystyle K=\sup _{t\in [0,1]}|B(t)|}
where B(t) is the Brownian bridge. The cumulative distribution function of K is given by[2]
Pr  ( K ≤ x ) = 1 − 2 ∑ k = 1 ∞ ( − 1 ) k − 1 e − 2 k 2 x 2 = 2 π x ∑ k = 1 ∞ e − ( 2 k − 1 ) 2 π 2 / ( 8 x 2 ) , {\displaystyle \operatorname {Pr} (K\leq x)=1-2\sum _{k=1}^{\infty }(-1)^{k-1}e^{-2k^{2}x^{2}}={\frac {\sqrt {2\pi }}{x}}\sum _{k=1}^{\infty }e^{-(2k-1)^{2}\pi ^{2}/(8x^{2})},}
which can also be expressed by the Jacobi theta function ϑ 01 ( z = 0 ; τ = 2 i x 2 / π ) {\displaystyle \vartheta _{01}(z=0;\tau =2ix^{2}/\pi )} . Both the form of the Kolmogorov–Smirnov test statistic and its asymptotic distribution under the null hypothesis were published by Andrey Kolmogorov,[3] while a table of the distribution was published by Nikolai Smirnov.[4] Recurrence relations for the distribution of the test statistic in finite samples are available.[3]
Under null hypothesis that the sample comes from the hypothesized distribution F(x),
n D n → n → ∞ sup t | B ( F ( t ) ) | {\displaystyle {\sqrt {n}}D_{n}{\xrightarrow {n\to \infty }}\sup _{t}|B(F(t))|}
in distribution, where B(t) is the Brownian bridge.
If F is continuous then under the null hypothesis n D n {\displaystyle {\sqrt {n}}D_{n}} converges to the Kolmogorov distribution, which does not depend on F. This result may also be known as the Kolmogorov theorem. The accuracy of this limit as an approximation to the exact cdf of K {\displaystyle K} when n {\displaystyle n} is finite is not very impressive: even when n = 1000 {\displaystyle n=1000} , the corresponding maximum error is about 0.9 % {\displaystyle 0.9\%} ; this error increases to 2.6 % {\displaystyle 2.6\%} when n = 100 {\displaystyle n=100} and to a totally unacceptable 7 % {\displaystyle 7\%} when n = 10 {\displaystyle n=10} . However, a very simple expedient of replacing x {\displaystyle x} by
x + 1 6 n + x − 1 4 n {\displaystyle x+{\frac {1}{6{\sqrt {n}}}}+{\frac {x-1}{4n}}}
in the argument of the Jacobi theta function reduces these errors to 0.003 % {\displaystyle 0.003\%} , 0.027 % {\displaystyle 0.027\%} , and 0.27 % {\displaystyle 0.27\%} respectively; such accuracy would be usually considered more than adequate for all practical applications.[5]
The goodness-of-fit test or the Kolmogorov–Smirnov test can be constructed by using the critical values of the Kolmogorov distribution. This test is asymptotically valid when n → ∞ {\displaystyle n\to \infty } . It rejects the null hypothesis at level α {\displaystyle \alpha } if
n D n > K α , {\displaystyle {\sqrt {n}}D_{n}>K_{\alpha },\,}
where Kα is found from
Pr  ( K ≤ K α ) = 1 − α . {\displaystyle \operatorname {Pr} (K\leq K_{\alpha })=1-\alpha .\,}
The asymptotic power of this test is 1.
Fast and accurate algorithms to compute the cdf Pr  ( D n ≤ x ) {\displaystyle \operatorname {Pr} (D_{n}\leq x)} or its complement for arbitrary n {\displaystyle n} and x {\displaystyle x} , are available from:
[6] and [7] for continuous null distributions with code in C and Java to be found in [6].
[8] for purely discrete, mixed or continuous null distribution implemented in the KSgeneral package [9] of the R project for statistical computing, which for a given sample also computes the KS test statistic and its p-value. Alternative C++ implementation is available from [8].
Test with estimated parameters[edit]
If either the form or the parameters of F(x) are determined from the data Xi the critical values determined in this way are invalid. In such cases, Monte Carlo or other methods may be required, but tables have been prepared for some cases. Details for the required modifications to the test statistic and for the critical values for the normal distribution and the exponential distribution have been published,[10] and later publications also include the Gumbel distribution.[11] The Lilliefors test represents a special case of this for the normal distribution. The logarithm transformation may help to overcome cases where the Kolmogorov test data does not seem to fit the assumption that it came from the normal distribution.
Using estimated parameters, the questions arises which estimation method should be used. Usually this would be the maximum likelihood method, but e.g. for the normal distribution MLE has a large bias error on sigma! Using a moment fit or KS minimization instead has a large impact on the critical values, and also some impact on test power. If we need to decide for Student-T data with df = 2 via KS test whether the data could be normal or not, then a ML estimate based on H0 (data is normal, so using the standard deviation for scale) would give much larger KS distance, than a fit with minimum KS. In this case we should reject H0, which is often the case with MLE, because the sample standard deviation might be very large for T-2 data, but with KS minimization we may get still a too low KS to reject H0. In the Student-T case, a modified KS test with KS estimate instead of MLE, makes the KS test indeed slightly worse. However, in other cases, such a modified KS test leads to slightly better test power.
Discrete and mixed null distribution[edit]
Under the assumption that F ( x ) {\displaystyle F(x)} is non-decreasing and right-continuous, with countable (possibly infinite) number of jumps, the KS test statistic can be expressed as:
D n = sup x | F n ( x ) − F ( x ) | = sup 0 ≤ t ≤ 1 | F n ( F − 1 ( t ) ) − F ( F − 1 ( t ) ) | . {\displaystyle D_{n}=\sup _{x}|F_{n}(x)-F(x)|=\sup _{0\leq t\leq 1}|F_{n}(F^{-1}(t))-F(F^{-1}(t))|.}
From the right-continuity of F ( x ) {\displaystyle F(x)} , it follows that F ( F − 1 ( t ) ) ≥ t {\displaystyle F(F^{-1}(t))\geq t} and F − 1 ( F ( x ) ) ≤ x {\displaystyle F^{-1}(F(x))\leq x} and hence, the distribution of D n {\displaystyle D_{n}} depends on the null distribution F ( x ) {\displaystyle F(x)} , i.e., is no longer distribution-free as in the continuous case. Therefore, a fast and accurate method has been developed to compute the exact and asymptotic distribution of D n {\displaystyle D_{n}} when F ( x ) {\displaystyle F(x)} is purely discrete or mixed [8], implemented in C++ and in the KSgeneral package [9] of the R project for statistical computing. The functions disc_ks_test(), mixed_ks_test() and cont_ks_test() compute also the KS test statistic and p-values for purely discrete, mixed or continuous null distributions and arbitrary sample sizes. The KS test and its p-values for discrete null distributions and small sample sizes are also computed in [12] as part of the dgof package of the R project for statistical computing. Major statistical packages among which SAS PROC NPAR1WAY [13], Stata ksmirnov [14] implement the KS test under the assumption that F ( x ) {\displaystyle F(x)} is continuous, which is more conservative if the null distribution is actually not continuous (see [15] [16] [17]).
Two-sample Kolmogorov–Smirnov test[edit]
Illustration of the two-sample Kolmogorov–Smirnov statistic. Red and blue lines each correspond to an empirical distribution function, and the black arrow is the two-sample KS statistic.
The Kolmogorov–Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. In this case, the Kolmogorov–Smirnov statistic is
D n , m = sup x | F 1 , n ( x ) − F 2 , m ( x ) | , {\displaystyle D_{n,m}=\sup _{x}|F_{1,n}(x)-F_{2,m}(x)|,}
where F 1 , n {\displaystyle F_{1,n}} and F 2 , m {\displaystyle F_{2,m}} are the empirical distribution functions of the first and the second sample respectively, and sup {\displaystyle \sup } is the supremum function.
For large samples, the null hypothesis is rejected at level α {\displaystyle \alpha } if
D n , m > c ( α ) n + m n m . {\displaystyle D_{n,m}>c(\alpha ){\sqrt {\frac {n+m}{nm}}}.}
Where n {\displaystyle n} and m {\displaystyle m} are the sizes of first and second sample respectively. The value of c ( α ) {\displaystyle c({\alpha })} is given in the table below for the most common levels of α {\displaystyle \alpha }
α {\displaystyle \alpha } 0.10 0.05 0.025 0.01 0.005 0.001
c ( α ) {\displaystyle c({\alpha })} 1.073 1.224 1.358 1.517 1.628 1.858
and in general[18] by
c ( α ) = − 1 2 ln  α . {\displaystyle c\left(\alpha \right)={\sqrt {-{\frac {1}{2}}\ln \alpha }}.}
Note that the two-sample test checks whether the two data samples come from the same distribution. This does not specify what that common distribution is (e.g. whether it's normal or not normal). Again, tables of critical values have been published. A shortcoming of the Kolmogorov–Smirnov test is that it is not very powerful because it is devised to be sensitive against all possible types of differences between two distribution functions. [19] and [20] showed evidence that the Cucconi test, originally proposed for simultaneously comparing location and scale, is much more powerful than the Kolmogorov–Smirnov test when comparing two distribution functions.
Setting confidence limits for the shape of a distribution function[edit]
Main article: Dvoretzky–Kiefer–Wolfowitz inequality
While the Kolmogorov–Smirnov test is usually used to test whether a given F(x) is the underlying probability distribution of Fn(x), the procedure may be inverted to give confidence limits on F(x) itself. If one chooses a critical value of the test statistic Dα such that P(Dn > Dα) = α, then a band of width ±Dα around Fn(x) will entirely contain F(x) with probability 1 − α.
The Kolmogorov–Smirnov statistic in more than one dimension[edit]
A distribution-free multivariate Kolmogorov–Smirnov goodness of fit test has been proposed by Justel, Peña and Zamar (1997).[21] The test uses a statistic which is built using Rosenblatt's transformation, and an algorithm is developed to compute it in the bivariate case. An approximate test that can be easily computed in any dimension is also presented.
The Kolmogorov–Smirnov test statistic needs to be modified if a similar test is to be applied to multivariate data. This is not straightforward because the maximum difference between two joint cumulative distribution functions is not generally the same as the maximum difference of any of the complementary distribution functions. Thus the maximum difference will differ depending on which of Pr ( x < X ∧ y < Y ) {\displaystyle \Pr(x<X\land y<Y)} or Pr ( X < x ∧ Y > y ) {\displaystyle \Pr(X<x\land Y>y)} or any of the other two possible arrangements is used. One might require that the result of the test used should not depend on which choice is made.
One approach to generalizing the Kolmogorov–Smirnov statistic to higher dimensions which meets the above concern is to compare the cdfs of the two samples with all possible orderings, and take the largest of the set of resulting K–S statistics. In d dimensions, there are 2d−1 such orderings. One such variation is due to Peacock[22] and another to Fasano and Franceschini[23] (see Lopes et al. for a comparison and computational details).[24] Critical values for the test statistic can be obtained by simulations, but depend on the dependence structure in the joint distribution.
In one dimension, the Kolmogorov–Smirnov statistic is identical to the so-called star discrepancy D, so another native KS extension to higher dimensions would be simply to use D also for higher dimensions. Unfortunately, the star discrepancy is hard to calculate in high dimensions.
Implementations[edit]
Kolmogorov - Smirnov Test (one or two sampled test verifies the equility of distributions) is well documented in many packages of statistical softwares and programms. The list of packages in some programms:
MATLAB has kstest in its Statistics Toolbox.
R's statistics base-package implements the test as ks.test {stats} in its "stats" package.
SAS implements the test in its PROC NPAR1WAY procedure.
Python (programming language) has an implementation of this test provided by SciPy[25] by Statistical functions (scipy.stats)
SYSTAT (SPSS Inc., Chicago, IL)
Java (programming language) has an implementation of this test provided by Apache Commons[26]
StatsDirect (StatsDirect Ltd, Manchester, UK) implements all common variants.
Stata (Stata Corporation, College Station, TX) implements the test in ksmirnov (Kolmogorov–Smirnov equality-of-distributions test) command. [27]
PSPP implements the test in its KOLMOGOROV-SMIRNOV (or using K-S shortcut function.
Excel runs the test as KSCRIT and KSPROB [28]
Kuiper's test
Shapiro–Wilk test
Anderson–Darling test
^ Stephens, M. A. (1974). "EDF Statistics for Goodness of Fit and Some Comparisons". Journal of the American Statistical Association. 69 (347): 730–737. doi:10.2307/2286009. JSTOR 2286009.
^ Marsaglia G, Tsang WW, Wang J (2003). "Evaluating Kolmogorov's Distribution". Journal of Statistical Software. 8 (18): 1–4. doi:10.18637/jss.v008.i18.
^ a b Kolmogorov A (1933). "Sulla determinazione empirica di una legge di distribuzione". G. Ist. Ital. Attuari. 4: 83–91.
^ Smirnov N (1948). "Table for estimating the goodness of fit of empirical distributions". Annals of Mathematical Statistics. 19 (2): 279–281. doi:10.1214/aoms/1177730256.
^ Vrbik, Jan (2018). "Small-Sample Corrections to Kolmogorov–Smirnov Test Statistic". Pioneer Journal of Theoretical and Applied Statistics. 15 (1–2): 15–23.
^ a b Simard R, L'Ecuyer P (2011). "Computing the Two-Sided Kolmogorov–Smirnov Distribution". Journal of Statistical Software. 39 (11): 1–18. doi:10.18637/jss.v039.i11.
^ Moscovich A, Nadler B (2017). "Fast calculation of boundary crossing probabilities for Poisson processes". Statistics and Probability Letters. 123: 177–182.
^ a b c Dimitrova DS, Kaishev VK, Tan S (2019). "Computing the Kolmogorov–Smirnov Distribution when the Underlying cdf is Purely Discrete, Mixed or Continuous". Journal of Statistical Software. forthcoming.
^ a b Dimitrova, Dimitrina; Kaishev, Vladimir; Tan, Senren. "KSgeneral: Computing P-Values of the K-S Test for (Dis)Continuous Null Distribution". cran.r-project.org/web/packages/KSgeneral/index.html.
^ Pearson, E. S. and Hartley, H. O., eds. (1972). Biometrika Tables for Statisticians. 2. Cambridge University Press. pp. 117–123, Tables 54, 55. ISBN 978-0-521-06937-3. CS1 maint: Uses editors parameter (link)
^ Shorack, Galen R.; Wellner, Jon A. (1986). Empirical Processes with Applications to Statistics. Wiley. p. 239. ISBN 978-0471867258.
^ Arnold, Taylor B.; Emerson, John W. (2011). "Nonparametric Goodness-of-Fit Tests for Discrete Null Distributions" (PDF). The R Journal. 3 (2): 34\[Dash]39.
^ "SAS/STAT(R) 14.1 User's Guide". support.sas.com. Retrieved 14 April 2018.
^ "ksmirnov — Kolmogorov–Smirnov equality-of-distributions test" (PDF). stata.com. Retrieved 14 April 2018.
^ Noether GE (1963). "Note on the Kolmogorov Statistic in the Discrete Case". Metrika. 7 (1): 115–116.
^ Slakter MJ (1965). "A Comparison of the Pearson Chi-Square and Kolmogorov Goodness-of-Fit Tests with Respect to Validity". Journal of the American Statistical Association. 60 (311): 854–858.
^ Walsh JE (1963). "Bounded Probability Properties of Kolmogorov–Smirnov and Similar Statistics for Discrete Data". Annals of the Institute of Statistical Mathematics. 15 (1): 153–158.
^ Eq. (15) in Section 3.3.1 of Knuth, D.E., The Art of Computer Programming, Volume 2 (Seminumerical Algorithms), 3rd Edition, Addison Wesley, Reading Mass, 1998.
^ Marozzi, Marco (2009). "Some Notes on the Location-Scale Cucconi Test". Journal of Nonparametric Statistics. 21 (5): 629–647. doi:10.1080/10485250902952435.
^ Marozzi, Marco (2013). "Nonparametric Simultaneous Tests for Location and Scale Testing: a Comparison of Several Methods". Communications in Statistics – Simulation and Computation. 42 (6): 1298–1317. doi:10.1080/03610918.2012.665546.
^ Justel, A.; Peña, D.; Zamar, R. (1997). "A multivariate Kolmogorov–Smirnov test of goodness of fit". Statistics & Probability Letters. 35 (3): 251–259. CiteSeerX 10.1.1.498.7631. doi:10.1016/S0167-7152(97)00020-5.
^ Peacock J.A. (1983). "Two-dimensional goodness-of-fit testing in astronomy". Monthly Notices of the Royal Astronomical Society. 202 (3): 615–627. Bibcode:1983MNRAS.202..615P. doi:10.1093/mnras/202.3.615.
^ Fasano, G., Franceschini, A. (1987). "A multidimensional version of the Kolmogorov–Smirnov test". Monthly Notices of the Royal Astronomical Society. 225: 155–170. Bibcode:1987MNRAS.225..155F. doi:10.1093/mnras/225.1.155. ISSN 0035-8711. CS1 maint: Uses authors parameter (link)
^ Lopes, R.H.C., Reid, I., Hobson, P.R. (April 23–27, 2007). The two-dimensional Kolmogorov–Smirnov test (PDF). XI International Workshop on Advanced Computing and Analysis Techniques in Physics Research. Amsterdam, the Netherlands. CS1 maint: Uses authors parameter (link)
^ "scipy.stats.kstest". SciPy SciPy v0.14.0 Reference Guide. The Scipy community. Retrieved 18 June 2019.
^ "KolmogorovSmirnovTes". Retrieved 18 June 2019.
^ "ksmirnov — Kolmogorov –Smirnov equality-of-distributions test" (PDF). Retrieved 18 June 2019.
^ "Kolmogorov-Smirnov Test for Normality Hypothesis Testing". Retrieved 18 June 2019.
Daniel, Wayne W. (1990). "Kolmogorov–Smirnov one-sample test". Applied Nonparametric Statistics (2nd ed.). Boston: PWS-Kent. pp. 319–330. ISBN 978-0-534-91976-4.
Eadie, W.T.; D. Drijard; F.E. James; M. Roos; B. Sadoulet (1971). Statistical Methods in Experimental Physics. Amsterdam: North-Holland. pp. 269–271. ISBN 978-0-444-10117-4.
Stuart, Alan; Ord, Keith; Arnold, Steven [F.] (1999). Classical Inference and the Linear Model. Kendall's Advanced Theory of Statistics. 2A (Sixth ed.). London: Arnold. pp. 25.37–25.43. ISBN 978-0-340-66230-4. MR 1687411.
Corder, G. W.; Foreman, D. I. (2014). Nonparametric Statistics: A Step-by-Step Approach. Wiley. ISBN 978-1118840313.
Stephens, M. A. (1979). "Test of fit for the logistic distribution based on the empirical distribution function". Biometrika. 66 (3): 591–595. doi:10.1093/biomet/66.3.591.
Hazewinkel, Michiel, ed. (2001) [1994], "Kolmogorov–Smirnov test", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Short introduction
KS test explanation
JavaScript implementation of one- and two-sided tests
Online calculator with the KS test
Open-source C++ code to compute the Kolmogorov distribution and perform the KS test
Paper on Evaluating Kolmogorov's Distribution; contains C implementation. This is the method used in Matlab.
Paper on Computing the Two-Sided Kolmogorov–Smirnov Distribution; computing the cdf of the KS statistic in C or Java.
Paper powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions; Jeff Alstott, Ed Bullmore, Dietmar Plenz. Among others, it also performs the Kolmogorov–Smirnov test. Source code and installers of powerlaw package are available at PyPi.
Continuous data
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Retrieved from "https://en.wikipedia.org/w/index.php?title=Kolmogorov–Smirnov_test&oldid=903105246"
Nonparametric statistics
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Last summer, I bought a bookshelf from Ikea. It looked simple in the picture, and the floor model was sturdy and seemingly uncomplicated. I loaded it in the car, brought it home, and started the assembly process. I am not a very "handy" person, and I am probably more comfortable in the kitchen than in the garage, but I can follow directions. So, after about a half an hour, my bookshelf was complete. I might have had to take it apart at one point when I realized that a main piece was on backwards. And, I might have had a few pieces leftover when I was done. Still, it looked pretty much like the picture, and it seemed sturdy enough to hold books. Had I not had directions to follow, I am sure that I would not have been as successful in my endeavor.
Unfortunately, not everything in life comes with directions. Take raising kids for instance. Wouldn't it be nice if upon leaving the hospital they asked you to sign a birth certificate, checked your car seat for proper installation, and handed you an up-to-date set of directions for raising a child - complete with new sections on social media and definitions for "flossing" and "TL;DR"? Unfortunately, that is not how it works. You do have to sign a birth certificate, and they do check your car seat (luckily there are directions for that), but there are no instructions on how to raise kids.
Your child reports to you that another child called them a "butthead" on the playground.
Call the other child's parents to let them know what their child said to yours, and arrange a time to meet in the morning so an apology can take place.
Ask your child how it made them feel. Ask them what they did about it. Ask them what tools they might use in the future if it happens again.
Email the teacher immediately and ask for a meeting.
This is a very normal situation, and none of the possible actions are wrong. Yet, each of them has the potential to take this situation in a dramatically different direction. As we talk about this, and other scenarios, we go down the path of different actions and talk about the positive and negative outcomes that might arise. This gives us the opportunity to highlight the importance of a strong home-school partnership, and helps to demystify some of the behaviors that kindergarten parents might experience.
Never be embarrassed to ask for advice from other parents or your school. Whatever you are experiencing with your child, someone else has gone through it.
Assume best intent. Parents and teachers (and kids) are all doing the best they can.
Take the time to respond and not react. Before you send that heated email, take a breath and sleep on it. You may feel different in the morning.
Let go of things. We call this "using your garbage can tool." Kids do and say dumb things. The same kid that called your child a butthead will likely be the one that they want to invite for a sleepover. Kids are great at letting go of things. Follow their lead.
I won't go so far as to call this a set of "directions," but following these guidelines can go a long way in avoiding some major parenting pitfalls. And, with a little luck, the final product - though it might look a little different than what you expected - is sure to be pretty awesome!


There is no place in all this world so wholesome and refreshing as a Christian home, a home where Christ is truly loved and honored.
This writer was brought up in such a home. There were ten of us: dad, mother and eight children. There was lots going on all the time, but a truly happy home it was, for dad and mother never let us get so busy with temporal things that we brushed eternal values aside.
On the basis that "man shall not live by bread alone, but by every word of God" (Luke 4:4), we read some small portion of the Bible before every meal, and had family devotions before retiring at night.
Result: all eight children have blessed the dear dad and mother who led them aright, morally and spiritually, and best of all, taught them the importance of trusting in the Savior who died for all our sins. More: five of the children and many of the grandchildren have given themselves for full time Christian service, and have become pastors, college deans, Christian writers and missionaries in various parts of the world.
"The Christian Home" is taken from the devotional email entitled "The Christian Home" I received from Berean Bible Society. I claim no credit to this post. Just want to share this wonderful devotional to those who can read it. Be blessed!
It is a blessing to be raised in a Christian family where Christ is sought to be the center of the household decisions. A blessing and a privilege as well, because we are expected to be an example of love and Christ-likeness to our neighbors.
God bless you! I grew up in a Christian home as well. I would say it's also a challenge to maintain a Christ-like home, lalo pag nag aaway na. hehe.


Vienna, Austria became popular for its sausages, which were called "Vienna sausages" or "wieners" (after "wien," the German for "Vienna"). Some forms include "wiener wurst" (little sausages), "wienies," and "weenies." The misspelling "weiner" is also common in America.
Vienna sausage is a variety of canned sausage. The term means essentially the same thing as Wiener, as the word "Wiener" means "Viennese" in German.
Canned Vienna sausages are generally made using a simplified adaptation of the process used to mass-produce other sausages. Meats, such as chicken, beef, and pork, are finely ground and mixed with salt and spices, especially mustard, and formed into a batter, which is poured into a long casing and smoked. The sausages are cooked, chopped into equal size segments, and placed into tins or jars, usually without the casings, and, with broth or brine added, processed the same as other canned goods.
Hot dogs are also called frankfurters, or franks for short (named after the city of Frankfurt, Germany, the original frankfurters are made of pork only), or wieners or weenies (named after the city of Vienna, Austria, whose German name is "Wien", the original wieners are made of a mixture of pork and beef). In Australia, the term frankfurt is used rather than frankfurter. A tiny version, called a cocktail frank or cocktail weenie, is sometimes served at parties and eaten on the end of a toothpick. In the German speaking countries, except Austria, hot dog sausages are generally called Wiener or Wiener Würstchen. (Würstchen means "little sausage") In Swiss German, it is called Wienerli; but, in Austria, the terms Frankfurter or Frankfurter Würstchen are used.
1. wiener schnitzel: see SCHNITZEL.
2. wienerwurst [G. wurst sausage]: = Vienna sausage s.v. VIENNA 1a. U.S.
1889 Gallup (New Mexico) Gleaner 27 Mar. 3/3 We.. are willing to bet our unpaid debts, against a weiner-wurst [sic] that the modest local of the Democrat blushed more than the bride when he saw her in the diaphanous costume he describes.
1899 F. NORRIS McTeague v. 75 The lunch baskets were emptied… There were wienerwurst and frankfurter sausages.
B. n. a. = wiener wurst above. Cf. WEINER. N. Amer.
1904 H. R. MARTIN Tillie iii. 34 I'm havin' fried smashed potatoes and wieners.
b. Comb. wiener roast N. Amer., a barbecue at which wieners are cooked and served.
1920 Outing July-Aug. 245/1 All over France they introduced the women war workers to American hikes, wiener roasts, camping in the open, and games of all sorts.
1935 Amer. Speech X. 159 'Weinies', 'Wienies', and 'Weenies' are also for sale.
= WIENER n. a. Cf. WEENY n.2, WINNY.
1911 Daily Colonist (Victoria, B.C.) 26 Apr. 7/3 Weinies, pretzels and coffee were served and German relishes.
1867 J. CHRISTISON Crime & Criminals 37 For a week longer he served at his usual business, which was that of peddling 'winnies', mostly among the saloons.
1914 B. TARKINGTON Penrod xix. 199 Winnies! Here's your hot winnies! Hot winny-wurst!
Vienna sausage, a small frankfurter made of pork, beef, or veal (cf. wienerwurst s.v. WIENER a. 2).
1958 Catal. County Stores, Taunton June 4 *Vienna Sausagesa tin 4/-.
Unless he carries about Vienna sausages in his portmanteau, he may freely pass even the gates of Leghorn.
Hot Wiener Wurst and cool Milwaukee lager at Henry's to-night.
The illness of a family, caused by eating wiener wurst, was attributed to trichina, but that belief did not obtain general credence until quite recently, when the head of the family mentioned.
Bill Henscal is doing big "wiener wurst" business.
"Wiener wust," is a common street cry in Cincinnati, being used by venders of Vienna sausage. These men have little stands at the street corner, provided with a vessel for keeping the sausage hot by means of steam, a box for German rye bread, and a jar for horseradish. For five cents they sell a steaming link of sausage, resting on a slice of bread, and horseradish sprinkled over it. The sausage is made of three parts beef to one of pork.
"Wiener wurst" is a common street cry in Cincinnati, being used by venders of Vienna sausage. These men have little stands at the street corners, provided wit ha vessel for keeping the sausage hot by means of steam, a box for German rye bread and a jar for horseradish. For five cents they sell a steaming link of sausage, resting on a slice of bread, with horseradish sprinkled over it. The sausage is made of three parts beef to one of pork.
A Philadelphia Girl Captures the "Wienerwurst" Man.
J. T. Schoonover went to Frank Jennings' sandwich stand last night and demanded a wienerwurst sandwich.
Weinerwurst sandwiches are served daily after 9 p. m. to customers at the Sazerac.


text:
PHN EXTRA: Olli Maatta Focused On Improving His Skating
Photo By Michael Miller
https://pittsburghhockeynow.com/phn-extra-olli-maatta-focused-on-improving-his-skating/
CRANBERRY TOWNSHIP, Pa. – Olli Maatta's face twisted. He had a hard time finding the words he wanted – and it wasn't an English-Finnish thing. How do you break down the complicated process of improving your skating?
"There's a lot of biomechanics and technical stuff. It's a lot of stuff," the Pittsburgh Penguins defenseman said during the early days of training camp at the UPMC Lemieux Sports Complex.
"It's tough to explain. Just staying on your skates, not necessarily having (physical) pressure on the ice. I feel like it helped me a lot."
Perhaps the most important aspect to Maatta's offseason work on his skating was simply the decision to make that a focus point. Maatta's strong, confident skating was one of the things that made him an attractive prospect before the Penguins made him the 22nd overall pick in the 2012 draft.
Introspectively, Maatta saw a decline that he wanted to address, and he was honest about it.
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Related Topics:Dave CruikshankFeaturedKris LetangOlli MaattaPittsburgh PenguinsShelly Anderson
PHN EXTRA: Justin Schultz Points, Confidence Dipped; New Partner Could Help
PHN EXTRA: New Guys Fine; Sidney Crosby Misses Pascal Dupuis
Shelly is the newest columnist and reporter for Pittsburgh Hockey Now. She was a Penguins beat writer for the Pittsburgh Post-Gazette and remains a contributor to The Hockey News. Catch her on Twitter @_shellyanderson


text:
Notre Dame's Brian Kelly: There's an 'Appetite' for Expanded College Football Playoff
Kelly is reportedly in favor of an eight-team format.
Notre Dame head coach Brian Kelly told reporters Saturday that he senses there is "an appetite to begin dialogue" surrounding expansion of the College Football Playoff, according to ESPN's Dan Murphy.
The No. 3 Fighting Irish (12–0, Independent) were one of four teams to be included in this year's postseason tournament, which has been in place for five seasons. Notre Dame was ranked third in the final College Football Playoff poll, beating out Big Ten champion Ohio State and Pac-12 champion Washington.
Kelly is reportedly in favor of an eight-team format that would enable each of the Power 5 conference champions to make the playoff, while also open at-large spots for other schools.
WEST: Wisconsin Athletic Director Barry Alvarez Calls for Expanded Playoff System
Kelly isn't the first prominent college football figure to publicly clamor for an expansion of the College Football Playoff this week. On Wednesday, Wisconsin athletic director Barry Alvarez reportedly said that "expansion is inevitable."
Notre Dame will face No. 2 Clemson in the Goodyear Cotton Bowl Classic on Dec. 29. In the other CFP matchup, No. 1 Alabama will play No. 4 Oklahoma in the Capital One Orange Bowl on Dec. 29.
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