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ULTRAVIOLET FLUORESCENCE PHOTOGRAPHY OF THE SHROUD OF TURIN
14 AUG 2020 FRENZ
V. D. Miller and S. F. Pellicori
One of the nondestructive techniques used to investigate the Shroud of Turin was ultraviolet fluorescence (UV) photography. This technique is able to detect organic and inorganic compounds by their integrated emission spectra and it is the complement of the more common technique of reflectance photography. Photographic data collection was one of many information resources designated by the Shroud of Turin Research Project1 (STURP) team for the investigation of the body image and blood stains. The goal of the team was to determine the nature of the body image and its cause.
The investigation in October 1978 followed the conclusion of the public exhibition held in celebration of the 400th anniversary of the Shroud's housing in Turin, Italy. That was the first public exhibition in 45 years and the first fullscale multidisciplinary study in the Shroud's history.2,3
The Shroud is a 4.4 by 1.1 meter piece of age-yellowed linen which displays the life-sized dorsal and frontal images of a man. The appearance of the visible image and the locations of the blood stains suggest parallels with the descriptions of Christ's crucifixion in the Scriptures. For this reason, the legend associated with the Shroud of Turin is that it is the burial cloth ofJesus of Nazareth. It has also been suggested that the image was painted in the 14th century. Since the historical record is complete back only to the 1350's, the veracity of the legend cannot be directly addressed. Obvious scorch and water marks can be pinpointed to a fire in 1532. Hypotheses such as artistic painting, for example, can be tested for agreement with the observations. The team was thus charged with the task of collecting multifaceted data of necessary and sufficient quality and quantity for testing various hypotheses.
The United States team, an independent group of 32 scientists and assistants, was equipped with instrumentation4 capable of detecting work produced by known artistic techniques and adequate to provide a broadly-based foundation of information. The instrumentation included x–ray transmission and fluorescence5 to detect high atomic
number elements expected for inorganic pigments, microscopy6 for visual and
photographic examination of details, photoelectric spectrophotometry7,8 for measurements of reflectance and fluorescence, photography9 through bandpass filters, infrared spectrometry10 and UV fluorescence photography documented here for the first time.
Figure 1A– Transmittance curves for the ultraviolet (UV) exciting filter cell used in front of the xenon source and for the UV barrier filter used over the camera lens.
B– Configuration of exciter and barrier filters for ultraviolet fluorescence photography. The exciter filter consisted of a Pyrex window and a filter cell containing a 1 cm path of the solution shown and a Corning 7-54 glass filter for absorption of the residual red leak. The Hoya L-42 filter served as a barrier filter transmitting only those wavelengths above 420 nm. C– Exciter filter cell attached to flash reflector.
Figure 2-Camera and Illumination positioned on support rail for indexing along the length of the Shroud and thus creating a complete mosaic of photographs according to the reference layout in Figure 3. A– Lamp heads (Norman 200 B) with liquid cell filter. B -AC power pack. C –EL Hasselblad camera with 70 mm back. D -Telescoping extention rod for locating rail equi-distant from Shroud frame. E –Leveling screws.
F -Centimeter scale with indexing marked for predetermined positions. G -Adjustable sliding index pointer for starting sequence.
Photographic procedure
To record the emission excited by ultraviolet, a special light source was assembled. For our experiment a filterwindow bandpass enabled wavelengths of 335 to 375 nm to be isolated from the sources for the exciting radiation. The two sources aimed at 45–degree angles from the camera-subject axis were 200 watt second xenon strobes with 15-cm reflectors. The film was to record only radiation emitted in the visible region of the spectrum, and none of the reflected, exciting UV. Consequently, the light source had to
be free of visible radiation. To achieve these conditions special excitation filters were constructed to fit on the 15-cm diameter strobe sources.
The filters consisted of a 1-cm path length containing a mixture of inorganic salts of transition metals 11 to absorb radiation above about 400 nm. One window of the liquid filter cell was Corning 9863 visible-absorbing UV–transmitting glass.
This 9863 filter was required to attenuate a small red leak in the exciter filter. The other window was pyrex. The isolated passband and out-of-band attenuation measured for the filter are shown in Figure 1. Since the fluorescences we sought were expected to be in the visible, the filter needed to attenuate to a level of 10– 4 since visible light from the xenon tubes would completely swamp the weak fluorescent signals. The reasons for using a liquid filter system were that no other filters such as multilayer coatings or ultraviolet transmission glass alone are able to define the required passband while possessing adequate rejection. Further, none of the standard filter materials could survive the heat of the xenon flash. Finally, the 15-cm size was beyond standard UV accessories.
The exciting UV energy which was partially reflected by the Shroud was prevented from reaching the film by a nonfluorescing, long-wavelength pass, UV absorbing glass placed in front of the lens (Figure 1). This barrier filter passed wavelengths greater than 410 nanometers.
The camera and light source assembly was moved along a rail parallel to the long dimension of the Shroud, which was mounted with its short dimension vertical (Figure 2). The long dimension was divided into eight 53.3-cm square areas for photography and later full-size reconstruction. The areas were intended to be coincident with the black–and–white color separation series taken at another time.
The sections were numbered from left to right, beginning at the dorsal feet end of the Shroud. The number-letter coordinate set corresponded with a master reference mosaic and is shown in Figure 3.
The camera was a Hassleblad EL with a 80 mm lens. The film used was Kodacolor 400 film, a color negative film with an exposure index of 400. Prints were then made on Kodak Ektacolor no. 78 paper.
Differences between the fluorescent record and white light photos were noted.
Assisted by laboratory data, interpretation of these differences provides insight into the nature and causes of the various markings on the Shroud, namely the body image, blood stains, and scourge, water and scorch marks. These interpretations can be compared with laboratory-produced simulations.
Detailed observations
Some general comparisons from color photographs of fluorescing colors and natural light colors are listed in Table I.
Differences are detailed in the following pages for each section of the Shroud under discussion. Section B through E by 1 through 4, for example, defines a rectangle according to the coordinates of the reference overlay on the Shroud. (See Figure 3 and the reduced size overlay in the text.)
Figure 3-Reference layout of the Shroud showing the numbered and lettered sections discussed in detail in the text.
Table I-Comparison between UV Fluorescence and Visible Reflectance Photographs
Figure 4– Section B through Eby 1 through 4 of the Shroud. A-UV fluorescence. B-white light reflectance photograph.
Dorsal feet area– B through E by 1 through 4 (Figure 4)
Some cloth fluorescent characteristics stand out as different from the white light appearance, namely creases, thread, and shadowing are less apparent in UV.
The striation in the weave pattern (warp versus weft) are enhanced in fluorescence.
There is a general decrease in cloth emission at the corners. The teflon coated magnets, quite visible in white light, are nonfluorescent. This signifies the rejection level of reflected light. The visual water marks are not detectible fluorescently, while the scorches around the burns emit reddish fluorescence.
Left foot-C through D by 1 through 2
Blood is red visually, but neutral to black (absorbing) fluorescently. Detailed shading in absorption in the blood in center of left foot. A triangular-shaped pattern is seen at the ball of the foot. Note the very dense absorption in the blood area at the left end of the rivulet from the heel: scorching might be associated. A fluorescing border in the blood now off the body image areas is seen.
A more distinct light border area is seen. The body image appears different from the blood in fluorescence, that is, it absorbs less intensely. The scourge marks have greater contrast in fluorescence than in white light and on the calf appear as lines rather than as dumbbell shapes as they do further up on the leg. Some scourges are not perceptible in the white light photo. The scourge Lines run parallel and diagonally from top left to bottom right. T he background cloth fluorescence is prominent between the leg images (C-D area). The absorbing water marks at 3 and B through E have Light border areas.
General dorsal areas– 4 through 6 (Figure 5)
Figure 5– Section B through E by 4 through 6. A-UV fluorescence. 8 -white light reflectance photograph.
Red fluorescence is seen around patches at left and right bounda ries.
There is a series of holes through t he Shroud cloth (through which the reinforcing backing cloth sewn to the Shroud after the fire can be seen). The densely burned borders of these burned holes show no emission. Where the more lightly scorched material matches the appearance of other scorched areas (around added patches, for example), the fluorescent appearance is quite different, that is, no emission is seen. The different appearances might relate to different generation mechanisms.
Calf areas of right and left leg Scourges favor orthogonal orientation in this area. As the thigh is approached, the scourges become scratchlike. On the right leg at C-5 and D-6, the scourges appear to be off the body image area. Weave striations are obvious in fluorescence. In D-6 and C-6, we note small areas of brightness between center burns in both em ission and reflection photos. The circular mark in the thighs (D-5 and C-5) resembling a scourge might be a scorch mark. Similarly, in D-7 and C-7, there is no fluorescence emission, but perhaps the marks have the same origin as the circular burn holes in this section.
At the boundaries, Band E, and a round the patches, the scorches display shading in red emission. These scorches appear different from the burn holes. The water stain, C-5 and D-5, did not disturb the scourge marks. In areas B t hrough E by 6-7, faint red-brown bands are apparent: they traverse the burn holes. Notice at the expected knee joint, 6, that there is no body image apparent and limited scourging.
Figure 6– Section B through E by 7 through 9. A-UV fluorescence. B-white light reflectance photograph.
Dorsal midsection area– 7 through 9 (Figure 6)
All the patched burn areas fluoresce reddish brown, including the water stain front. Other white light water boundaries are indistinguishable in fluorescence. The scourges orient orthogonally and are distinctly absorbent against the fluorescent background linen. The emission of the linen is not uniform. Across the small of the back the rivulets of blood are absorbing; see also D-9 and C-9. There are, some lighter border areas associated with the blood flow. Some of the densest marks within the blood flow area might be scorches. In area D-8, the blood boundaries fade in fluorescence. At E-8 and C-8 the stains at the inner boundary of the large patches appear to be mirror images.
Two small circular stains at C-7 and D–7 are mirror images and visualiy resemble weak scorches. In fluorescence these stains are absorbing. Note also lighter boundary areas associated with water marks. The body image (nonfluorescing) is very dense at the scapula and rib cage.
Scourges are apparent through the scorched shoulder areas above the patches. Many scourges have fluorescing bordering areas.
Dorsal head and neck area and ventral head area– 10 through 12 by B through E (Figure 7)
Figure 7– Section B through E by 10 through 12. A-UV fluorescence. B-white light reflectance photograph.
At E and Band at patches 11 and 12, red fluorescing scorched areas are obvious. The brightly fluorescing yellowgreen donut-shaped areas to the right of patch 11– 12 at E and B appear to be scorches. They are mirrored elsewhere at symmetrically located fold sections. The faint water stain between the head images has light blue boundaries in fluorescence. The cloth weave striation is an apparent nonuniformity. The blood stains on the dorsal head area are bounded by brighter areas. A smudge or scourge appears to the right of the general blood flow on the dorsal head. Faintscorch pattern is visible in the light blood stains. At C-D by 11-12 a smudge resembling blood is visible between the head images. The dorsal body B image is more distinct than the ventral image. At the center of the dorsal head, a blue fluorescence is noted. This has a different color than the body image.
Figure 8– Section B through E by 13 through 15. A– UV fluorescence. B-white light reflectance photograph.
Head and chest-13 through 15 by D through C (Figure 8)
Scorches near the patches emit reddish brown fluorescence. The water stain boundary below patches at C–15 and E–15 appear to contain reddish fluorescent material as from scorches, while those at C and D at 15 (abdomen) do not contain fluorescing material. The lower left arm blood stains, B and C at 16, have light border areas. Through the scorches of B at 14 and 15, upper left arm, can be seen blood or scourges. The upper area of the left shoulder shows faint blood, scourge and body detail. The diffusely appearing
scourge marks below the central water stain, C and D at 16, become more distinct
(scratch-like) near C–15 and D–15. Scourges are diagonal and orthogonal, with a scratch characteristic predominant on the left. The face is more strongly bounded by the weave pattern on its left side than on its right, C and D at 13. Going beyond this feature, no image is discernible. The blood streaks in the hair are denser on the right side and have fluorescing boundaries, C and D at 13. In comparison with the general body image, the beard and mustache are denser. ln fact, the density is greatest on the left portion of the beard and mustache and more diffuse on the right. A distinct boundary is present at the lower left. The lower lip appears to have a fluorescent boundary. On the right shoulder, the blood stains are in very sharp detail, with the lower stain broken into dots. Compare
this area with some of the scourges on the right side. Circles of yellow–green fluorescence are associated with these wounds.
Ventral hands and thighsarea 16 through 19 (Figure 9)
Scorches show red fluorescence except for those associated with the sets of three holes which have heavily burned borders. Plumes of pyrolyzed materials pointing toward the feet are seen associated with the burned holes. At 19 the plume pointing toward the hands fluoresces red. Some shading from red to yellow fluorescence can be seen. The water mark above the knees at 18 has an absorbant edge with density gradations.
Some fluorescing bordering can be seen also. In white light, however, this water stain is not prominent. The fluorescent color is brown as opposed to grey. The water stain situated above the series of holes to the right side has very little emission. Some of the water stains are better defined in fluorescence, others are not. The blood and body image are similar in the fluorescence photos; i.e., grey and non-emitting. Notice the clear fluorescing borders around the hand wound blood stains. As is true of scourges elsewhere, the scourge wounds are more distinguishable in the fluorescence photos. As the upper thigh area is approached, however (see 19), the scourges become more diffuse. Often scratches are contained within the diffuse areas. Some scourge marks appear only in the fluorescence photos: examples are noted between the hands and forearm areas.
Around the knuckle of the left hand a slight blood flow can be seen. The body image absorption, especially arm and thigh, is greater on the left side of the body. There is a detail located where the genitals would be expected below the intersection of the hands. The dark patch below the wrist wound appears distinct from the body image. It is not understood. The fingers possess more contrast by fluorescence photography. The differences among water stain appearances might be due to differing material content, with some containing mobile pyrolysis products.
Figure 10– Section B through E by 19 through 22. A-UV fluorescence. B-white light reflectance photograph.
Ventral feet, knees and thighs-19 through 22 (Figure 10)
A very faint body outline is discernible in this section, even in fluorescence photos. The feet are not defined. The leg outline and scourge markings are limited by a weave line appearing blue in fl uorescent emission where the weave direction changes.This is an area of"no-print."
The central water stain at B and C by 18 and 19 is contrast-enhanced by fluorescence: it absorbs strongly against the emitting background. While the water stain at D-20 has fluorescing border areas, the opposing one at A-20 does not. Also, the one at D-22 has an unusually wide absorbing boundary. As in the other scourged a reas, the scourges run diagonally left to lower right, and both diffuse and scratch-like marks, some perpendicular to the leg, are visible. See the left leg at B-20 and 21. Some scourges appear to be bounded by the central water stain. No scourges can be found on the ankles.
On the feet, two blood stain areas are distinguishable on the right foot; the smaller one is denser, the larger has a fluorescing border area. Curious less densely absorbing flows without definite boundary trail from the blood spots. They do not resemble the usual blood characteristics. The smal l circular mark above the water boundary at D-22/21 has the fluorescent colors of a scorch: red grading to a yellow border. To the upper right a 2-inch diameter stain containing three dark lines appears by nuorescence contrast, but not by white light. Wax drops seen in this area are bright. nuorescers colored yellow, or green. At the lower edge, D-22, two sharp-edged marks visible as dark brown emit bright white in nuorescence.
Discussion-Laboratory experiments
In fluorescence photographs most of the details are visible in contrast with the Shroud linen, which itself fluoresces. With the exception of lightly scorched areas and some water stained areas, the Shroud features absorb UV energy without visible emission. Compared with modern linen, the Shroud linen fluoresces less brightly.
It emits a yellow–green color. Modern linen can be artificially aged by baking at high temperatures (125°-150° C) to the point where its reflected color and fluorescent emission approach those of the Shroud.7 When foreign materials are applied to the linen, a reaction which results in locally visible darkening of the linen can be stimulated by air baking as above.
These experiments7 have led to the interpretation that the body image is the result of locally accelerated dehydration/oxidation and conjugation of the cellulose molecular structure. Images produced in hours at high temperature are comparable in both reflectance and UV stimulated emittance to images produced at normal temperatures during longer time intervals (years?). Laboratory-produced images were photographed using the same equipmentas was used in Turin. Exposure to sunlight of wavelengths less than 340 nm influences the rate and degree of cellulose degradation.
Laboratory data for whole blood displayed total absorption, which is in agreement with the Shroud data.
Weak scorches, which in white light have densities and colors similar to body image areas, show a significant difference with UV fluorescence photography.
Scorches emit a reddish brown fluorescence while the body image is nonfluorescent. The significance of this difference is evident in relation to the suggestion that the body image was caused by contact with a hot statue or was scorched by other means. Laboratory-produced scorches emit a bright greenish-yellow fluorescence if they were produced in air and reddish if produced under conditions of limited available oxygen. The scorches
associated with the fire of 1532, during which the Shroud was involved, attest to the rapid consumption of the available oxygen. 12 Their reddish emission is probably due to furfurals, which can be produced under such conditions.
Linen lightly scorched by a soldering iron in air shows the green–yellow emission, often distributed in plumes of deposited pyrolysis products. We demonstrated in one experiment that the material of the plumes could be transported by water, but the underlying scorched cellulose retained a bright yellow–green fluorescence. This demonstration together with the observed absence of body image fluorescence is strong evidence against the cause for the body image being a scorch.
A quite frequent hypothesis is that the body image was painted. The binders used in paints as early as the 14th century would be made of proteinaceous materials, animal collagen being a favored material; egg white and gelatin are other examples. But these collagens would inherently be contaminated by fluorescing amino acids. 13 Random sampling of book bindings and illustrations from the 14th and 15th centuries were observed to emit bright fluorescence when excited by long-wave mercury vapor lamp excitation.
Microchemical analyses on fibrils retrieved from the Shroud have shown the absence of paints, pigments, stains, dyes and protein in body image areas.14
The sharp detail revealed for the first time, particularly in the scourges, suggests that intimate cloth-body contact occurred. The detail (and contrast) is only slightly less prominent on the front than on the dorsal image, indicating that the large difference in weight for each side had only a minor influence on the imprinting of the scourges. This observation is contrary to what might be intuitively expected, and it might be a clue to some future understanding of the image production mechanism.
The occurrence of contact could also have transferred substances present on the skin to the cloth where they stimulated the cellulose alteration process and caused an image of the body to develop as local darkening of the linen.7
Hypotheses such as a scorch cause or paint are contradicted by the fluorescence photography results.
UV fluorescence photography has revealed some near-invisible details, many of which require explanation. For example, the pattern of distinct burn holes has characteristics unlike the burn damage attributed to the 1532 fire. Areas in the weave where the image density abruptly decreases (e.g., sides of the face) might actually contain very faint images which possibly could be retrieved by using stimulating radiation of shorter wavelengths. The property of the linen thread that didn't develop image density should also be discovered. The 8-cm side strip running the length of the Shroud shows weft bands that are continuous with the main body of the Shroud. Similar appearances result from backlighting and low-energy radiography. The suggestion is that this strip was not separated from the main body over its entire length.
Many of these unexplained details might relate to the history of the Shroud.
Another feature requiring explanation is the lighter bordering area seen with many bloodstained a reas. The interpretation is that blood serum is present. It might have acted to retard the image development reactions associated with the body image. Fibrils from many water stain fronts and from the area between the head images contain blood particles.14 Further discussions are in preparation.15
We appreciate the assistance given by D. Devan and other members of the STURP team, and also acknowledge the cooperation extended by the church officials in Turin. J. Druzik, Conservation Center, Los Angeles County Museum of Arts, critically reviewed the manuscript.
About the authors– Vernon Miller is Head of t he Scientific and Industrial Photography Department at the Brooks Institute of Photography, Santa Barbara, California. He was the chief scientific photographer for the STURP team in Turin, and has employed a variety of image processing techniques to the photographic data obtained.
Samuel Pellicori is an optical physicist with the Santa Barbara Research Center. He has been evaluating and simulating in the laboratory some of the spectrophotometric, fluorometric and microscopic data he collected in Turin.
Address correspondence to Samuel Pellicori, Santa Barbara Research Center, 75 Coromar Drive, Goleta, California 93017.
1. Proceedings of the 1977 U.S. Conference of Research on the Shroud ofTurin, Holy Shroud Guild, 294 E. 150 St., Bronx, NY 10451.
2. Kenneth F. Weaver, "The Mystery of the Shroud," National Geographic 157, 730 (1980).
3. B. J. Culliton, "Science Investigates the Shroud of Turin," Science 201, 235 (1978).
4. E. J. Jumper and R. W. Mottern, "Scientific Investigation of the Shroud of Turin," Appl. Opt. 19, 1909 (1980).
5. R. A. Morris, L. A. Schwalbe and J. R. London, "X-Ray Fluorescence lnvestigation of the Shroud of Turin," X-Ray Spectrometry 9, No. 2, 40 (1980).
6. Samuel Pellicori and Mark S. Evans, "The Shroud of Turin Through the Microscope," Archaeology 34, 34, Jan/Feb 1981.
7. S. F. Pellicori, "Spectral Properties of the Shroud of Turin," Applied Optics 19, 1913 (1980).
8. Roger Gilbert, Jr., and Marion M. Gilbert, "Ultraviolet-Visible Reflectance and Fluorescence Spectra of the Shroud of Turin," Applied Optics 19, 1930 (1980).
9. V. Miller and D. Lynn, "Photography of the Turin Shroud," Science and Technology, Feb. 1981 (in Dutch).
10. J. S. Accetta and J. S. Baumgart, "Infrared Reflectance Spectroscopy and Thermographic Investigations of the Shroud of Turin," Appl. Opt. 19, 1921 (1980).
11. S. F. Pellicori, "Transmittances of Some Optical Materials for Use Between 1900 and 3400 A," Appl. Opt. 3, 361 (1964).
12. R. N. Rogers in Reference 1, p. 133.
13. Eric J. Jumper, John P. Jackson, John H. Heller, Alan D. Adler, Samuel F. Pellicori and Raymond N. Rogers, "A Comprehensive Examination of the Various Stains and Images on the Shroud of Turin," American Chem. Soc. Proc. on Archaeological Chem. (1982). in preparation.
14. J. H. Heller and A. D. Adler, "A Chemical Investigation of the Shroud of Turin," submitted to Journal of Forensic Sciences.
15. L.A. Schwalbe and R. N. Rogers, "Physics and Chemistry of the Shroud of Turin: Summary of the 1978 Investigation," in preparation.
shroud of turin photos


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Uni Bonn
Meat import ban in Africa hurts local population
The EU regularly exports large quantities of poultry meat to West African countries. These exports have been criticized for harming importing countries in West Africa and exacerbating poverty there. The reason: Cheap imports depress the local price of chicken, making life difficult for local smallholders. Researchers at the Universities of Bonn and Göttingen have now used the example of Ghana to calculate the effects that would result if the country were to significantly increase its import tariffs for poultry meat or even stop imports completely. The result: Prices would indeed rise domestically, but most local households would not benefit. The study has been published in the journal Food Security.
European Football Championship with side effects
The 2020 UEFA European Football Championship, which was played in 2021, had a very different impact on the infection dynamics of the coronavirus pandemic in different participating countries. The extent to which the rates of infection and death from Covid-19 increased depended primarily on the pandemic situation in the country at the start of the championship. This was concluded by physicists in an analysis of epidemiological data. The study involved the Max Planck Institute for Dynamics and Self-Organization in Göttingen, the Max Planck Institute for Physics in Munich, as well as the Universities of Bonn and Göttingen and the PUNCH4NFDI consortium in the German national research data infrastructure NFDI. The study was published in Nature Communications.
Physical effect also valid in the quantum world
Physicists at the University of Bonn have experimentally proven that an important theorem of statistical physics applies to so-called "Bose-Einstein condensates." Their results now make it possible to measure certain properties of the quantum "superparticles" and deduce system characteristics that would otherwise be difficult to observe. The study has now been published in Physical Review Letters.
Glial cells help memory along
There are two fundamentally different cell types in the brain, neurons and glial cells. The latter, for example, insulate the "wiring" of nerve cells or guarantee optimal working conditions for them. A new study led by the University of Bonn has now discovered another function in rodents: The results suggest that a certain type of glial cell plays an important role in spatial learning. The German Center for Neurodegenerative Diseases (DZNE) was involved in the work. The results have now been published in the journal Nature Communications.
First selection round successfully completed:
The Cologne/Bonn Academy in Exile (CBA), founded in the summer of 2022 supports researchers from Ukraine, who have fled the war in their country. It additionally supports researchers from Belarus and Russia, who had to flee their countries due to their opposition to the war. The researchers have been invited to continue their scientific work at the Universities of Cologne and Bonn. Considering the potential of Ukraine to become a member of the European Union in the future, the work of the researchers and the academy will focus on the expansion of regional specific knowledge and European integration, as well as their incorporation and that of their research into the European scientific community while preserving national ties.
Three vehicles on fire at University sports facility
Three vehicles, including an electric transporter and a small tractor, were destroyed last night in a fire at the University sports facility on Nachtigallenweg. The vehicles had caught fire for as yet unexplained reasons.
University and Faculty of Catholic Theology mourn Benedict XVI.
The Rheinische Friedrich-Wilhelms-Universität Bonn and its Faculty of Catholic Theology mourn the loss of its former theology professor, Prof. Dr. Joseph Aloisius Ratzinger, Pope Emeritus Benedict XVI, who died on December 31, 2022, at the age of 95. "The University of Bonn mourns not only an important figure in contemporary history, but also a great theologian and pope whose work and ministry will remain influential in many ways," wrote Rector Prof. Dr. Dr. h.c. Michael Hoch and Dean Prof. Dr. Dr. Jochen Sautermeister in a joint obituary for the deceased.

redpajama_set_name: RedPajamaCommonCrawl


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\section{Introduction}
A convincing theory of fermion masses and mixings is one of the most salient omission in the current description of particle physics and at present it does not seem to be on the horizon. All of the charged fermion masses and mixing parameters in the quark sector are experimentally known to a very good precision \cite{pdg}. Even in the neutrino sector, remarkable experimental progress has resulted in advancement in our knowledge of the properties of neutrinos. Theoretical  attempts, on the other hand, are limited mostly to phenomenological approaches, wherein one goes for building phenomenological models having the potential for  predictions, in tune with the latest data, which later on become the guiding steps for more ambitious theories.

In the standard electroweak model, the masses of the charged fermions, weak mixing angles and the complex phase parameter causing CP violation enter as free parameters. Further
insights into the dynamics which determine the masses and mixing angles call for steps beyond the
electroweak standard model. In the absence of specific hints towards the underlying dynamics
one is invited to consider specific symmetry schemes which could reduce the number of free
parameters in the fermion sector and eventually provide hints towards further dynamical
details of the mass generation mechanism \cite{famsym}.

In this regard, one of the successful approach is the ``texture zero" approach, initiated implicitly by Weinberg \cite{weinberg} and explicitly by Fritzsch \cite{frz}, wherein certain entries of the mass matrix are exactly zero, such matrices are usually referred to as ``texture specific mass matrices". The language of texture zeros has proven to be very useful in establishing experimentally testable relations between the ratios of quark masses and the flavor mixing angles \cite{mmreview}.  Recently it has been shown \cite{shivali} that the present refined data of quark masses and mixing angles unambiguously rules out the original Fritzsch ansatz as well as all of its texture 6 zero variants. Further, also the present data rules out all possible texture 5 zero hermitian mass matrices \cite{5zero}. On the other hand, it has been observed over the years that  texture 4 zero mass matrices, similar to the original Fritzsch ansatz have always been compatible with the quark mixing data \cite{mmreview,4zero}. It has also been shown that out of all possible texture 4 zero mass matrices, compatible with weak basis transformations \cite{weakbasis}, there is a unique set of matrices along with its permutations  matrices which has the best possible compatibility with the quark mixing data. This is also borne out by a very recent extensive analysis of  of  texture 4 zero mass matrices \cite{aakriti}. This brings into focus  the issue whether it is possible to reduce the free parameters of these matrices so as to facilitate the task of model builders. The purpose of the present paper is to explore this possibility, particularly in relation to the phase parameters of these having implications for the CP violating parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.

The paper is organized as follows. In Section \ref{qmm}, while presenting the analysis of Fritzsch-Xing matrices with updated values of quark masses and the latest results of the CKM flavor mixing parameters, we also give the notations and basic expressions needed and general formalism adopted for the analysis. In Section \ref{mqmm}, we formulate texture 4 zero mass matrices with minimal parameters, thus enhancing the predictive power of these mass matrices. After confirming the validity of this set of mass matrices, we also discuss the hierarchy exhibited by mass matrix elements in our model. The details regarding the parameter space spanned by the free parameters have been presented and the correlations between these have been discussed. In the Section
\ref{secpre}, we present the predictions of this set of mass matrices for the angles of the reference unitarity triangle (UT), Jarlskog's rephasing invariant parameter $J$ and CP violating phase $\delta$. In Section  \ref{sensitivity}, we study the relative dependence of CKM parameters on the quark masses. Finally, Section \ref{sum} summarizes our main conclusions.

\section{The Fritzsch-Xing Texture 4-zero Quark Mass matrices: An updated analysis} \label{qmm}
Before performing an updated and complete numerical analysis of the parameter space
of mass matrices with four texture zeros, let us briefly review the relations
between the parameters of mass matrices and the observable quantities.
For the three generations of quarks,  the quark mass terms are given as
\begin{equation}
{\overline u}_L M_u u_R  + {\overline d}_L M_d d_R\,,
 \label{mc} \end{equation}
where $u_{L(R)}$ and  $d_{L(R)}$ are the left-handed (right-handed)
 quark fields and $M_u$ and  $M_d$ are the mass matrices for the  up sector
$(u,c,t)$ and down sector $(d,s,b)$ respectively.
The mass matrices  can be  diagonalized  by
the following bi-unitary transformations :
\begin{equation} V_{u_L}^{\dagger}M_u V_{u_R} = M_u^{diag} \equiv {\rm Diag}\,
(m_u,m_c,m_t)\,;
\label{ou} \end{equation}
\begin{equation} V_{d_L}^{\dagger}M_d V_{d_R} = M_d^{diag} \equiv {\rm Diag}
\,(m_d,m_s,m_b)\,;
\label{od} \end{equation}
 where $M_q^{diag}~(q=u,d)$ are real and diagonal, while $V_{q_L}$ and
  $V_{q_R}$ are unitary $3 \times 3$ matrices. The quantities $m_u, m_d$ etc. denote the
  eigenvalues of the mass matrices, i.e. the physical
quark masses.
 The quark mixing matrix, connecting mass eigenstates to the weak eigenstates,
referred to as the Cabibbo-Kobayashi-Maskawa
matrix \cite{ckm} is given as,
\begin{equation}  V_{\rm CKM} =  V_{u_L}^{\dagger} V_{d_L}\,=  \left(
\begin{array} {ccc}
V_{ud} & V_{us} & V_{ub} \\
V_{cd} & V_{cs} & V_{cb} \\
V_{td} & V_{ts} & V_{tb} \\ \end{array}
\right)\,, \label{mix} \end{equation}
 where $V_{ud}$ gives the amplitude of the process $u \rightarrow d +
W$ and similarly for the other elements. Thus, apart from the quark masses, the elements of $V_{\rm CKM}$ constitute the
low energy observable quantities through which one can get clues
about the structure of the mass matrices, which are completely arbitrary in Standard model.  The  $V_{\rm CKM}$, by definition, is a  unitary
matrix,  hence can be expressed in terms of
 three real angles and six phases. Out of
the six phases, five can be re-absorbed into the quark fields in
Eq.(\ref{mc}). Therefore, one is left with only
one non-trivial phase
which is responsible for CP violation in the SM.
There are several parametrizations of the  $V_{\rm CKM}$,
however the most commonly used
parametrization is the standard parametrization, also advocated  by PDG \cite{pdg},
\begin{equation} V_{{\rm CKM}} =
 \left(
\arraycolsep=1.4pt
 \begin{array} {ccc} c_{12} c_{13} & s_{12} c_{13} &
  s_{13}e^{-i\delta} \\
  -s_{12} c_{23} - c_{12} s_{23} s_{13}e^{i\delta} &
 c_{12} c_{23} - s_{12} s_{23}s_{13}e^{i\delta}
  & s_{23} c_{13} \\
  s_{12} s_{23} - c_{12} c_{23} s_{13}e^{i\delta} &
  - c_{12} s_{23} - s_{12}c_{23} s_{13}e^{i\delta} &
  c_{23} c_{13} \end{array}
 \right),  \label{ckm1}  \end{equation}
  with $c_{ij}={\rm cos}\,\theta_{ij}$ and
   $s_{ij}={\rm sin}\,\theta_{ij}$.  In the PDG representation,  sin$\delta \neq 0$
implies the existence of  CP violation.

The Fritzsch-Xing quark mass matrices (texture 2-zero for $M_u$ and texture 2-zero for $M_d$) are presented below,
\begin{equation}M_u= \begin{pmatrix}
0&A_u&0\\A^*_u&D_u&B_u\\0&B_u^*&C_u
\end{pmatrix};~~
M_d= \begin{pmatrix}
0&A_d&0\\A_d^*&D_d&B_d\\0&B_d^*&C_d
\end{pmatrix},
\label{eq:ourMM}
\end{equation}
where $A_u=\lvert A_u\rvert e^{i \alpha_u}, \,A_d=\lvert A_d\rvert e^{i \alpha _d}, \,B_u=\lvert B_u\rvert e^{i \beta_u}, \,B_d=\lvert B_d\rvert e^{i \beta_d}$, such that the combined texture of quark sector is texture 4-zero.

\vskip 0.2cm
The diagonalizing transformations for these matrices can easily be obtained in terms of quark  masses and free parameters $D_u,\, D_d,\, \phi_1=\alpha_u-\alpha_d$ and $\phi_2=\beta_u-\beta_d.$ The details of the diagonalization equations for these mass matrices can be found in our earlier work \cite{diagon}.
Thus, in total, there are 10 parameters in the above set of matrices to describe the six quarks masses and four mixing parameters.

Before discussing the details of our analysis, we present the latest quark masses and mixing data. Since the observed parameters for the CKM mixing matrix are fitted at the electroweak energy scale
 $\mu = m_Z$, we have taken the quark masses also at $m_Z$ energy scale \cite{Qmasses}, and are given in Table \ref{tabinp}.

\begin{table}
\begin{center}
\caption{Quark masses at $m_Z$ energy scale  \cite{Qmasses} and mixing parameters as given by  global fit results by PDG \cite{pdg}.}
\begin{tabular}{ll} \hline
 $m_u$ & $1.23\pm 0.21$ MeV \\
 $m_c $& $0.620 \pm 0.017 $ GeV \\
 $m_t$ &$168.26 \pm 0.75$ GeV  \\
$m_d $& $2.67 \pm 0.19$ MeV\\
$ m_s$ &$ 53.16 \pm 4.61$ MeV\\
$m_b$  & $2.839 \pm 0.026$ GeV\\
$\lvert V_{us}\rvert $ & $0.22650 \pm 0.00048$ \\
$\lvert V_{ub}\rvert $ & $0.00361^{+0.00011}_{-0.00009}$ \\
$\lvert V_{cb}\rvert $ & $0.04053^{+0.00083}_{-0.00061}$\\
$ \sin 2\beta $ & $0.699 \pm 0.017$ \\
 \hline
\end{tabular}\label{tabinp}
\end{center}
\end{table}

For the mass matrices given in Eq. (\ref{eq:ourMM}), the CKM matrix can be obtained in terms of quark masses and free parameters $D_u, D_d, \phi_1$ and $\phi_2$. For the analysis, we use the quark masses given in Table \ref{tabinp} and scan their full ranges at 1$\sigma$, while the phases are scanned in the range [$-\pi,\pi$]. Thereafter, we calculate the CKM elements $\lvert V_{us}\rvert , \; \lvert V_{cb}\rvert , \lvert V_{ub}\rvert $ and angle $\beta$ of the UT. We keep the parameter sets, in which the value of each of these four observables is reproduced within the 1$\sigma$ interval of error-bars, as given by the global fit results by Particle Data Group (PDG) \cite{pdg} and presented  in Table \ref{tabinp}.

We choose these four mixing parameters, because their values have been determined to a very good degree of accuracy. The set of matrices given in Eq.(\ref{eq:ourMM}), successfully reproduces the three observed CKM elements and angle $\beta$ given in Table \ref{tabinp} in the parameter ranges given in Table \ref{tabpara}.

\begin{table}[h]
\begin{center}
\caption{Parameter ranges for the quark mass matrices given in Eq.(\ref{eq:ourMM}) that reproduce the mixing
parameters given in Table \ref{tabinp}.}
\begin{tabular}{cccc}
 \hline
$D_u\,(GeV)$~ & ~$D_d\,(GeV)$ &$\phi_1$& $\phi_2$ \\
$19.0-61.0$~ & ~$0.3-0.9$& $69.0\degree - 122.0\degree$ & $2.0\degree - 7.2\degree$ \\
\hline
\end{tabular}
\label{tabpara}
\end{center}
\end{table}

Angle $\beta$ refers to one of the inner angles of the CKM unitarity triangle described by the orthogonality relation $$ V_{ud}V_{ub}^{*} + V_{cd}V_{cb}^{*} + V_{td}V_{tb}^{*}
  =  0\,, $$ in the complex plane. The three
inner angles of this triangle are defined as,
 \begin{eqnarray}
  \alpha &\equiv &{\rm arg} \left[
-\frac{V_{td}V_{tb}^{*}}{V_{ud}V_{ub}^{*}} \right],\nonumber\\
\beta &\equiv &{\rm arg} \left[
-\frac{V_{cd}V_{cb}^{*}}{V_{td}V_{tb}^{*}} \right],\nonumber\\
\gamma &\equiv& {\rm arg} \left[
-\frac{V_{ud}V_{ub}^{*}}{V_{cd}V_{cb}^{*}} \right].   \label{angle}
\end{eqnarray}

  Another interesting measure of CP violation is the Jarlskog's rephasing invariant parameter $J$.
   The significance of ${J}$
     lies in the fact that all the CP violating effects in the SM
     are proportional to it as well as it is independent of the
     representation of CKM matrix. For hermitian quark mass matrices, $J$ can be obtained
using the commutator of mass matrices   \cite{jarlskog}, for example,
\begin{equation} iC \equiv [M_u,M_d] \, , \end{equation}
 such that
 \begin{eqnarray} \textrm{Det} C &=&-2J(m_t-m_c)(m_c-m_u)(m_u-m_t) \nonumber \\
 & & (m_b-m_s)(m_s-m_d)(m_d-m_b). \label{eq:detC} \end{eqnarray}
In parallel with the usage of commutators encountered in quantum mechanics, the commutator of hermitian mass matrices is a measure of the simultaneous diagonalization of the matrices, that is, its non zero value ensures mismatch in the diagonalization of the mass matrices, which in turn implies $CP$ violation.   Using Eq.(\ref{eq:detC}), one can easily express the rephasing invariant $J$, in terms of the mass matrices, $M_u$ and $M_d$.

  One can also express $J$ in terms of the $V_{\rm{CKM}}$ elements, as \begin{equation} J \sum_{\gamma , l} \epsilon_{\alpha \beta \gamma}\epsilon_{j k l } =\textrm{Im}[V_{\alpha j} V_{\beta k} V_{\alpha k}^* V_{\beta j} ^*]. \end{equation}
Using the standard parametrization, given in Eq.(\ref{ckm1}), $J$ can be expressed in terms of the CKM mixing angles, $\theta_{12}, \theta_{23} \text{ and } \theta_{13}$, and $CP$ violating phase, $\delta$, as
\begin{equation} J= s_{12}s_{23}s_{13}c_{12}c_{23}c_{13}^2 \sin\delta. \label{eq:deltaformula}\end{equation}
Therefore,
\begin{equation}
\footnotesize{
\delta = \sin^{-1} \left( \frac{- \textrm{Det} C}{2(m_t-m_c)(m_c-m_u)(m_u-m_t)(m_b-m_s)(m_s-m_d)(m_d-m_b)  s_{12}s_{23}s_{13}c_{12}c_{23}c_{13}^2} \right).}
\label{eq:dfromJ}
\end{equation}

\noindent
Thus, the $CP$ violating phase $\delta$ can be obtained in a rephasing invariant manner using the commutator of mass matrices.
In Table \ref{tabpr1}, we present the predictions of the mass matrices given in Eq. (\ref{eq:ourMM}) for the other two angles of the unitarity triangle i.e. $\alpha$ and $\gamma$ and for  $J$ and $\delta$.  From the Table, we observe that the ranges of $ \alpha,\,\gamma,\,J$ and $\delta$
are quite wide, however these include their ranges obtained from the global analyses  and the experimental limits \cite{pdg}.

\begin{table}[h]
\begin{center}
\caption{Predictions of the quark mass matrices given in Eq.(\ref{eq:ourMM}).
}
    \begin{tabular}{ccc}
\hline
$ \alpha$ & $66.2\degree - 113.7\degree$  \\
$\gamma$ & $44.7\degree -  92.3\degree$\\
$J$ & $(2.30 - 3.39)\times 10^{-5}$\\
$\delta$ &  $45.0\degree - 90.0\degree$\\ \hline
\end{tabular}\label{tabpr1}
 \end{center}
\end{table}

\section{Texture 4-zero Quark Mass matrices with minimal parameters} \label{mqmm}
 A figure of merit for any mass matrix model is its predictability power, which is maximal when a minimal number of free parameters are introduced. Using simplicity and the requirement of maximal predictability as guiding principles, we are led to consider if we can reduce the number of parameters further in the set of mass matrices given in Eq.(\ref{eq:ourMM}). To this end, we have tried various combinations, for example, we considered some of the elements as zeros, e.g. one can put (2,2) or (2,3) or (3,3) element as zero, however this does not reproduce CKM matrix within its limits. Getting rid of one of the phases $\phi_1$ or $\phi_2$, also does not lead to reproduction of compatible CKM matrix elements.

\begin{figure}[h]
 \centering
 \includegraphics[width=.8\textwidth] {cont.pdf}
 \caption{Contours of $\lvert V_{us}\rvert , \lvert V_{cb}\rvert , \lvert V_{ub}\rvert $ and $\sin2\beta$ in $\phi_1-\phi_2$ plane, for the mean values of quark masses and central values of allowed ranges of $D_u$ and $D_d$. The solid lines are for the lower limit of the ranges mentioned in the Table \ref{tabinp}, while the dashed lines are for the upper limit.}
 \label{fig:contours}
 \end{figure}

 In Fig. \ref{fig:contours}, we have plotted contours of $\lvert V_{us}\rvert , \lvert V_{cb}\rvert , \lvert V_{ub}\rvert $ and $\sin2\beta$ in $\phi_1-\phi_2$ plane for the mean values of quark masses and central values of allowed ranges of $D_u$ and $D_d$ given in Table \ref{tabpara}. The solid lines are for the lower limit of the ranges mentioned in the Table \ref{tabinp}, while the dashed lines are for the upper limit. The figure reveals several interesting points. For example, it   suggests that $\lvert V_{us}\rvert $ is not sensitive to variation in $\phi_2$, while it is very sensitive to variation in $\phi_1$. On the other hand, $\lvert V_{cb}\rvert $ is not sensitive to variation in $\phi_1$, while it is very sensitive to variation in $\phi_2$. $\lvert V_{ub}\rvert $ and $\sin 2\beta$ are sensitive to both $\phi_1$ and $\phi_2$. However, the most important observation is that angle $\phi_1$ is close to $90\degree$, while angle $\phi_2$ is very close to $0\degree$, where these strong constraints are majorly put by $\lvert V_{us}\rvert $ and $\lvert V_{cb}\rvert $, respectively. We also find that a non zero value of $\phi_2$ is very crucial to reproduce angle $\beta$. A quick look at Fig. \ref{fig:contours} motivates us to consider the possibility $\phi_1 = \phi_2 + 90\degree$, which we have investigated in detail below. As discussed earlier, our endeavor is to reduce the number of free parameters in mass matrices and hence we now present texture 2-zero parallel structure for the up and down quark mass matrices, with one less parameter than the matrices given in Eq. (\ref{eq:ourMM}), for example
\begin{eqnarray}
& &M_u= \begin{pmatrix}
0&\lvert A_u\rvert e^{i (\beta_u +\pi/4)}&0\\\lvert A_u\rvert e^{-i (\beta_u +\pi/4)}&D_u&\lvert B_u\rvert e^{i \beta_u}\\0&\lvert B_u\rvert e^{-i \beta_u}&C_u
\end{pmatrix};~~ \nonumber \\
& & M_d= \begin{pmatrix}
0&\lvert A_d\rvert e^{i (\beta_d -\pi/4)}&0\\\lvert A_d\rvert e^{-i (\beta _d -\pi/4)}&D_d&\lvert B_d\rvert e^{i \beta_d}\\0&\lvert B_d\rvert e^{-i \beta_d}&C_d
\end{pmatrix}.
\label{eq:newMM}
\end{eqnarray}
The mixing matrix corresponding to above mass matrices can be obtained in terms of the quark masses and free parameters
  $D_u,\, D_d$ and $\phi_2=\beta_u-\beta_d.$
Thus, in our proposed model we consider only one phase, i.e. $\phi_2$ to reproduce the CKM elements and angle $\beta$ of the UT.
As before, we scan the parameter space of $D_u, D_d$ and $\phi_2$ and keep the parameter ranges, in which the value of each observable is reproduced within the $1\sigma$ interval. We find that this simple \textit{ansatz} is able to reproduce the CKM elements, angles of UT, $J$ and $\delta$ well within their ranges given in PDG, in the parameter ranges given in Table \ref{tab:res3}. \par
\begin{table}[h]
\centering
\caption{Parameter ranges for the mass matrices given in Eq. (\ref{eq:newMM}) that reproduce the mixing
parameters given in Table \ref{tabinp}.}
\begin{tabular}{ccc}
\hline
$D_u\,(GeV)$~~ & ~~$D_d\,(GeV)$ & $\phi_2 $\\
$17.0-51.5$ & $0.25-0.75$ & $2.5\degree - 7.7\degree$\\
\hline
\end{tabular}
\label{tab:res3}
\end{table}
Once the allowed ranges of these three parameters are obtained, we can evaluate various quantities of the CKM paradigm. We begin with presenting the allowed ranges of real parts of the mass matrices $M_u \text{ and } M_d$,
\begin{eqnarray}
M_u^r&=&\begin{pmatrix}
0&0.027 - 0.035&0\\
0.027 - 0.035 & 17-51.5 & 51.47 - 78.26\\
0 & 51.47 - 78.26 & 115.88 -150.91
\end{pmatrix};~~ \nonumber \\
M_d^r&=&\begin{pmatrix}
0 & 0.012 - 0.015 & 0\\
0.012 - 0.015 & 0.25 - 0.75 & 0.88 - 1.30 \\
0 & 0.88- 1.30 & 2.02 - 2.56
\end{pmatrix}.
\label{eq:MMnum}
\end{eqnarray}
In the CKM paradigm, we notice several points of importance. First, the quark masses are strongly hierarchical, $m_{u,d }\ll m_{c,s} \ll m_{t,b}$, with the hierarchy of `up' sector being much stronger. Second, the CKM matrix elements also exhibit a strong hierarchy, i.e. $\lvert V_{ub}\rvert  < \lvert V_{td}\rvert \ll \lvert V_{ts}\rvert  < \lvert V_{cb}\rvert \ll \lvert V_{cd}\rvert  <\lvert V_{us}\rvert  < \lvert V_{cs}\rvert  < \lvert V_{ud}\rvert  < \lvert V_{tb}\rvert $, indicating the suppression of off-diagonal elements in comparison to diagonal ones. Therefore, we expect our analysis to manifest these strong hierarchies as well, i.e., the mass matrix elements are expected to follow the hierarchy $(3, 3) \gg (2, 3) \gg (2, 2) \gg (1, 2)$. However, our results in Eq.(\ref{eq:MMnum}) show that the hierarchy followed in both up and down sector is $(3, 3) \gtrsim (2, 3)\gtrsim (2, 2) \gg (1, 2)$, i.e. except for (1,2) element, the hierarchy observed between the mass matrix elements is weak.
Fig. \ref{fighier} clearly depicts the hierarchy followed by mass matrix elements, wherein
we show the obtained ranges of the mass matrix elements.
\begin{figure*}
 \centering
 \includegraphics[width=.75\textwidth] {hier.pdf}
 \caption{The ranges of mass matrix elements for both $M_u$ and $M_d$, depicting the hierarchy observed.}
 \label{fighier}
 \end{figure*}
Various authors have also considered 'weakly' hierarchical mass matrices to reproduce 'strongly' hierarchical mixing angles \cite{our4zero}.
 For instance, in Reference \cite{Xing2004}, Xing \textit{et al.} find $\lvert B_i\rvert /C_i \sim D_i/\lvert B_i\rvert  \sim 0.24$ for the case of both up and down  mass matrices. However, in Reference \cite{1501.06346}, Xing and Zhou find a new part of the parameter space, corresponding to $C_i \sim \lvert B_i\rvert  \sim D_i$. Both of these possibilities are covered by the set of mass matrices formulated by us in Eq. (\ref{eq:newMM}). To understand the reason to realize strong hierarchy in the elements of CKM matrix obtained from the weakly hierarchical mass matrix elements, we present the approximate expressions for the  off diagonal  CKM element  $V_{cb}$ below. We have used the approximation $m_{u,d }\ll m_{c,s} \ll m_{t,b}$ to arrive at the following:
\begin{equation}
  V_{cb}  \approx  -\sqrt{\frac{(m_t-D_u)(D_d+m_s)}{m_t m_b}}+e^{i \phi_2}\sqrt{
\frac{(D_u+m_c)(m_b-D_d)}{m_t m_b}}\,.\end{equation}
Numerical analysis shows that (i) $\phi_2$ being very small and the assumption $\phi_1 = \phi_2 + 90\degree$ as well as (ii) the lower right corner of the $M_u$ and $M_d$ being weakly hierarchical (as presented in Eq. (\ref{eq:MMnum})) ensure that $\lvert V_{cb}\rvert$ is sufficiently small to be in its experimental range. The free parameters   $D_u$ and $D_d$ of our mass model, being in the range  given in Eq. (\ref{eq:MMnum}) have a profound role in reproducing $\lvert V_{cb}\rvert$ and other off diagonal elements of CKM matrix. If the mass matrices given in Eq. (\ref{eq:newMM}) are taken to be  strongly  hierarchical, the off diagonal elements of CKM matrix turn out to be larger than  their experimental ranges. This issue has also been extensively discussed in a recent paper by Fritzsch et al. \cite{frzrev}, wherein they have studied the correlations between quark mass and flavor mixing hierarchies for Texture 4-zero Fritzsch-Xing quark mass matrices.

Apart from the hierarchy between the elements of $M_u$ or $M_d$, it is also desirable to discuss the correlations amongst the free parameters of $M_u$ and $M_d$. In Fig. \ref{figcorr}, we present the complete parameter space spanned by the free parameters, $D_u, D_d \text{ and } \phi_2$ in our model. We find that there is a strong correlation between mass matrix element (2,2) of up and down sector, i.e., $D_u$ and $D_d$. Further, the correlation between $D_u$ and $\phi_2$ and between $D_d$ and $\phi_2$ is very similar, hinting towards an underlying symmetry in up and down sectors.
In the middle right panel, we have plotted the parameter space available to $\delta$ with respect to $\phi_2$. We see a very strong correlation between $\delta$ and $\phi_2$. The shaded region corresponds to the limits on $\delta$ by the present global range, i.e. $\delta = (72.1^{+4.1}_{-4.5})\degree$ \cite{pdg}. We find that  the global range of $\delta$  is compatible with $\phi_2$ to be around $6\degree$.
Furthermore, the scatter plots in the lowest panel of Fig.  \ref{figcorr}, show very interesting correlations between some of the flavor mixing observables.
We find that  $\delta$ is correlated to $\lvert V_{us} \rvert$, clearly a result of lesser number of free parameters in our model due to the added assumption of
$\phi_1 = \phi_2 + 90\degree$. These correlations might be useful to   explore the underlying correlations between the quark mass spectrum and the flavor mixing pattern. Also, there is an  obvious linear correlation between  $\alpha$ and $\delta$ owing to the the unitarity triangle relation $\alpha+\beta+\gamma=\pi$.
The grey shaded regions in these plots indicate the 1$\sigma$ experimental ranges \cite{pdg} for these observables.

 \begin{figure*}
 \centering
   \includegraphics [width=.8\textwidth]{corr.pdf}
 \caption{The top and middle panels show the parameter space spanned by the free parameters of our mass matrices model given in Eq. (\ref{eq:newMM}), while the lowest panel displays the
correlations between   $\lvert V_{us} \rvert$ and $\delta$ and between $\alpha$ and $\delta$.}
 \label{figcorr}
 \end{figure*}

\begin{figure*}  \centering
 \includegraphics [width=1.0\textwidth]  {contnew.pdf}
 \caption{(a) Contours of $\lvert V_{us}\rvert , \lvert V_{cb}\rvert , \lvert V_{ub}\rvert $ and $\sin2\beta$ in $D_u$ and $\phi_2$ plane, for mean values of quark masses and $D_d = 0.4$, for the matrices given in Eq.(\ref{eq:newMM}). The solid lines are for the lower limit of the range mentioned in the Table \ref{tabinp}, while the dashed lines are for the upper limit. (b) The zoomed in region of (a) in the allowed range.}
 \label{figcontnew}
 \end{figure*}

 In Fig. \ref{figcontnew}(a), we have plotted the contours of $\lvert V_{us}\rvert , \lvert V_{cb}\rvert , \lvert V_{ub}\rvert $ and $\sin2\beta$ in $D_u$ - $\phi_2$ plane, for mean values of quark masses and $D_d =0.4$. The Fig. \ref{figcontnew}(b) depicts the zoomed in region of the same figure for better clarity. We infer that the precision determination of $\sin2\beta$ (red lines) and $\lvert V_{cb}\rvert $ (blue lines) will significantly restrict the allowed range of $D_u$. However, $\lvert V_{us}\rvert $ (black lines) does not put strong constraints on $\phi_2$ or $D_u$. We also find that CKM element $\lvert V_{ub}\rvert $ (green lines) loosely restricts $D_u$. The phase $\phi_2$ is restricted by  $\lvert V_{cb}\rvert ,\,\lvert V_{ub}\rvert $ and  $\sin2\beta$. These conclusions remain valid, even when the value of $D_d$ is varied in its allowed range. Thus, a more precise determination of $\sin 2\beta$ and $V_{CKM}$ elements will result in an even more restricted range of $\phi_2$, which would further yield a more precise evaluation of $CP$ violating phase $\delta$ as $\phi_2$ has interesting implications for the $CP$ violating phase $\delta$, as emphasized above.

\subsection{Predictions for CKM matrix, UT angles, $J$ and $\delta$}\label{secpre}
The mass matrix we formulated in Eq.(\ref{eq:newMM}), allows us to calculate the ranges of elements of the CKM mixing matrix using the methodology discussed earlier. the CKM matrix obtained is given as
\begin{eqnarray}
V_{CKM}=\begin{pmatrix}
0.9739 - 0.9741 & 0.2260 - 0.2270 & 0.00352 - 0.00372 \\
0.2258 - 0.2269 & 0.9731- 0.9733 & 0.0399- 0.0414\\
0.0070 - 0.0099 & 0.03889 - 0.04081 & 0.9991- 0.9992
\end{pmatrix}.
\end{eqnarray}
The above ranges are well consistent with the current global fit by PDG \cite{pdg}. The other two interior angles, $\alpha$ and $\gamma$, of the UT  can be evaluated from Eq.(\ref{angle}) to be
\begin{equation}
\alpha =(66.4 - 113.6)\degree , \;
\gamma = (44.9 - 92.1)\degree ,
\end{equation}
while the experimental value of $\beta$ was used as a constraint to check the viability of mass matrices. In order to evaluate Jarlskog's invariant rephasing parameter $J$ and $CP$ violating phase $\delta$, we use Eqs. (\ref{eq:detC}) and (\ref{eq:dfromJ}) to obtain
\begin{equation}
J = (2.30 - 3.39) \times 10^{-5}, \quad \delta = (44.9 - 92.1)\degree.
\end{equation}

The above ranges are quite wide and include the ranges given by the global fit analysis and experiments \cite{pdg}. Similar results for $CP$ violating phase and other CKM parameters have been obtained in the literature. For example, in Reference \cite{2002.09152}, authors obtain $\delta = (87.9) \degree$ as best fit value for the case of a 4-zero textures having the interplay of $\mu - \tau$ reflection symmetry. Similarly in Reference \cite{1912.07573}, authors present five different  viable models of texture zeros originating from modular symmetry and obtain the best fit value of $\delta= (69.2 \pm 3.1)\degree$.
Thus, our model, despite having only one phase parameter, is not only consistent with other such analyses, but also gives an excellent fit to most of the CKM parameters, which is phenomenologically very encouraging.
\begin{figure*}[t!]
 \includegraphics[width=1.\textwidth]{sens.pdf}
 \caption{Dependence of $\lvert V_{us}\rvert $, $\lvert V_{ub}\rvert $, $\lvert V_{cb}\rvert $ and $\beta$ on quark masses $m_u$(orange), $m_c$(cyan), $m_t$(black), $m_d$(red), $m_s$(blue), $m_b$(green).The x-axis of each plot corresponds to the 1$\sigma$ variation in the quark masses, while the shaded region   corresponds to the experimental value of that particular mixing parameter at 1$\sigma$, as given in the Table \ref{tabinp}. }
 \label{figsens}
 \end{figure*}
\subsection{Sensitivity of CKM elements on quark masses}\label{sensitivity}
To understand the role of precision determination of the quark masses for the mass matrix model formulated by us, given in Eq. (\ref{eq:newMM}), we have shown the variation of $\lvert V_{us}\rvert $, $\lvert V_{ub}\rvert $, $\lvert V_{cb}\rvert $ and $\sin 2\beta$ with respect to the quark masses in Fig. \ref{figsens}.

The x-axis of each plot corresponds to the variation in the quark masses  $m_u,\, m_c,\, m_t,\, m_d,\, m_s$ and $m_b$, shown respectively by orange, cyan, black, red, blue and green lines. Each quark mass is varied from its minimum to maximum value in the $1\sigma$ range given in Table \ref{tabinp}. The shaded region in each plot corresponds to the experimental value of that particular mixing parameter at 1$\sigma$, as given in the Table \ref{tabinp}. A quick look at the Fig. \ref{figsens} indicates that $\lvert V_{us}\rvert $ is most sensitive to the variation in the masses $m_d \text{ and } m_s$, while $\lvert V_{ub}\rvert $ shows maximum sensitivity to $m_u$ along with $m_d$ and $m_s$. Similarly, $\lvert V_{cb}\rvert $ and $\beta$ are most sensitive to variation in $m_s$ and $m_b$. Since the measurement of light quark masses are not as precise as measurement of heavy quarks, therefore, further refinement in the measurement of these quark masses and CKM parameters will help in eliminating many of the quark mass models.

\section{Summary and conclusion}\label{sum}
Motivated by the extensively used texture 4 zero Fritzsch-Xing  quark mass matrices, which are very successful in describing the CKM phenomenology, we formulate these with minimum possible free parameters. In the proposed structure, these quark mass matrices contain only one free phase compared with the usually considered  two phases. We study the implications of this particular set of texture 4 zero mass matrices  for the CKM phenomenology, particularly for the CP violation parameters,  $J$       and corresponding phase $\delta$. We find that these matrices  very well reproduce not only the CKM matrix but also the  angles of the UT,  $J$ and  $\delta$   well within their experimental and global fit ranges. We observe that except for the element (1,2), the matrix elements in both up and down sector follow a weak hierarchy, for example,  $(3, 3) \gtrsim (2, 3)\gtrsim (2, 2) \gg (1, 2)$. We find that there is a strong correlation between mass matrix element (2,2) of up and down sector, i.e.,  $D_u$ and $D_d$. Further, the correlation between $D_u$ and $\phi_2$ and between $D_d$ and $\phi_2$ is very similar, hinting towards an underlying symmetry in up and down sectors. We also infer that $\phi_2$ is strongly restricted by $\lvert V_{us}\rvert $ while $D_u$ and $D_d$ are primarily restricted by the limits $\sin 2\beta$ and $\lvert V_{cb}\rvert $. Due to a very strong correlation between the $CP$ violating phase $\delta$ and $\phi_2$, a precise measurement of $\delta$ will constrain the phase structure of the model further. The investigation of the sensitivity of various CKM elements on quark masses shows that a precision measurement of quark masses has the potential to constrain the model to a good extent.

In conclusion, it can be said that even in the absence of  theoretical justification,  mass matrices  with fewer parameters are  not only simple, but also more predictive and serve as a useful guide for model building and calls for a theoretical investigations  to understand the underlying symmetries. Further, it remains to be seen whether this texture can also be applied to the lepton sector.

\section*{Acknowledgements}
NA and MG would like to thank the Chairman, Department of Physics, Panjab University, Chandigarh  for providing facilities to work.
MK and MR would like to thank the Director, UIET,  Panjab University, Chandigarh  for providing facilities to work.  MK also acknowledges the financial support provided by Department of Science and Technology (DST), Govt. of India (Grant No. DST/INSPIRE Fellowship/2017/IF170125).

redpajama_set_name: RedPajamaArXiv


text:
Antonio de Valbuena, född 1844 i Pedrosa del Rey (León), död 1929, var en spansk författare.

Valbuena begagnade pseudonymerna Juan Paseante, Venancio González och 'Miguel de Escalada. Som politisk skriftställare framträdde han först i karlisttidningen "La Lealtad" och 1868 med en broschyr Sursum corda, vari han häftigt angrep revolutionen och förfäktade, att den enda lösningen vore en monarki Don Carlos.

I den av Valbuena ledda tidningen "La buena causa" fortsatte han sin kamp för karlismen, tills han 1870 måste emigrera till Frankrike. Vid återkomsten därifrån utgav han i Bilbao tidningen "La voz de Vizcaya", som emellertid snart blev indragen, varefter han i 5 år var medarbetare i Madridtidningen "El Siglo futuro".

Valbuena ägnade sig även åt litterär och språklig kritik med Ripios aristocráticos, Ripios académicos, Ripios vulgares, Ripios ultramarinos och med Fe de erratas del Diccionario de la Academia, en kritik av spanska akademiens ordboksarbete av 1884. För övrigt publicerade Valbuena odet A Zumalacárregui och novellsamlingarna Capullos de novela och Novelas menores.

Källor

Spanska journalister
Spanska kritiker
Litteraturkritiker
Spanska poeter
Spanskspråkiga poeter
Spanska novellförfattare
Spanskspråkiga novellförfattare
Spanska författare under 1800-talet
Födda 1844
Avlidna 1929
Män
Ugglan

redpajama_set_name: RedPajamaWikipedia


I absolutely love to have my tummy rubbed! I love it so much that I will melt in your arms while you do it. Don't you want me to be the newest addition to your family? I will have a complete nose to tail vet check and my vaccinations will also be up to date. Choose me and I promise to make a lifetime of memories with you. I can't wait to leap in your arms and be yours forever!"


There's a lot to life. Life is fascinating and has lots of pieces – choices. The key to living the life you choose is embracing your power, creating your opportunities and seizing those moments to create and dream your life.
Here's what I know for sure from my experience of grasping life by all it has to offer and living it with gusto . . .
1) Gotta grab that bomb pop – I believe that Bomp Pops are the true elixir of life and are best obtained while chasing down the ice cream man. What's your Bomb Pop of life?
2) Character – Live it, learn it, love it – I believe character is everything. Character will get you everywhere you want to go – even to the places you don't know that you want. You may not always get what you thought you wanted at first, but you always get what you really wanted all along.
3) Work hard, play hard – I believe hard work pays off, but you gotta make work fun! Life is too short – dance enjoy, be happy with whatever you do. You have the choice on how you want to play it. It's your dance floor.
4) Where there's a will, there's a way – I believe where there is a will, there is a way. You can do anything you set your mind to.
5) You are perfect, just the way you are – I believe we are all perfect just the way we are. Not just me, but you too! So let's get crackin' and do this thing! Whatever you want to do, know that you are perfect just the way you are, and with that knowledge, you can do anything.
6) Syncronicities are the breadcrumbs of life – I believe everything happens for a reason, that the things that happen for "some reason" are the money shots of life. That's where opportunity lies. Just follow the breadcrumbs.
7) Life is best when lived in the moment – I believe death is not to be feared. Like with any of life's challenges, live life in the moment and embrace the journey. You've got this – you can do it!
8) Grief should be honored – I believe that grief is a beautiful process that should be honored and savored. It shows our beauty as a human being, and each person's grief is as unique and as beautiful as a snowflake. There is no right, no wrong and there is no judgment in grief.
9) Fear is our friend – I believe that the idea "good things coming to those who wait" was written by someone who had too much fear to go for it. Sure you can be patient, but don't let it paralyze you. It's o.k. to be afraid, have fear and be honest about it. So you've got fear, so what? Grab fear's hand and run like hell towards your goal!
11) Write your own story and don't take anything personally – I believe that freedom and happiness come with not taking anything personally. What others do, say or believe is about them, not about you. They do not define you or your life. Focusing on others gives away your power. What do *you* want? Only you can write and create your own story. What story will you write?
12) Life is best lived on the edge…take a chance, make your move – I believe there's something to be said for living life a little on the edge – try anything once, try different things and see what you like, what you love and what really makes your socks go up and down. Take a chance. Make your move. If you can say it, you can do it. Freedom gives you opportunity.
13) There is infinite love in the world… I believe there is infinite love in the world and a web of amazing connections.
14) Learn it. Live it. Love it… One of my mottos reflecting my philosophy in life, which pretty much sums up all of the above!
What do you know for sure? How are you living your life?
Live your life. Embrace your power. Dream your life.
To schedule a 30 minute complimentary "Let's Get Started" session…a "Dream Your Life" one hour life coaching session…or a "Power Up My Life" package of six sessions….just email me at ravins52252@mypacks.net. You can read more on this site HERE. Or interested in a shamanic healing session, past life regression or other session? You can find more info on this site HERE and then just send me an email to schedule.
I look forward to all we can accomplish together! Let's get started!


text:
NEWS.WALES
Cases At Llandudno Magistrates Court - 08/10/19
Saturday 16th Jan 2021
At Llandudno Magistrates Court yesterday (08/10/19) Mr Chris Atherton of 8 Church Close, Penrhyn Bay, Llandudno, LL30 3LR was found guilty in his absence of failing to licence 21 Hawarden Road, Colwyn Bay, fined £1,000 and ordered to pay £100 legal and £98.25 investigative costs with a victim surcharge of £100. A total of £1,298.25
21 Hawarden Road, Colwyn Bay is a House in Multiple Occupation (HMO) and is required to be licensed under the Council's HMO Additional Licensing Scheme which applies to Colwyn Bay. Mr Atherton has failed to licence the property.
Also at Llandudno Magistrates Court yesterday (08/10/19), Mr Alan O'Reilly of 14 Lon Olwen, Kinmel Bay, Conwy, was found guilty in his absence of failing to license 10 Rhiw Bank Avenue, Colwyn Bay. He was fined £1,000 and ordered to pay £100 legal and £163.75 investigative costs with a victim surcharge of £100 – a total of £1,363.75
Cllr Charlie McCoubrey, Conwy County Borough Council's Cabinet Member for Housing and Regulatory, said, "Licensing of Houses in Multiple Occupation (HMO) is important as it raises management and amenity standards, thereby protecting both the tenants and the local community. Conwy County Borough Council is committed to raising the standards of HMOs and, as these cases clearly show, we won't tolerate landlords who disregard their responsibilities."
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text:
by vrchr | Jun 7, 2017 | It's Not Black and White |
Valuable Resources is a boutique of innovative professionals focused in 3 C's:
Culture Transformation
Compliance Education
Regardless if you're a Trump supporter or otherwise, despite the talk we've been hearing to "Make America Great Again" and the unrealistic promise to build "an impenetrable physical wall on the southern border" of the United States, realistically we know that people with diverse backgrounds will continue to come into this country. Further, they will be hired as employees. With this as our reality, employers must continue to comply with the Immigration Reform and Control Act of 1986, verifying employment eligibility by properly and timely by completing an I-9 for each and every employee.
The United States Citizenship and Immigration Services (USCIS) is an component of Homeland Security. The USCIS manage all administrative functions of processing applications, and petitions. For example, immigrant visa petitions, naturalization petitions, asylum applications, and refugee applications. In addition, the USCIS also makes adjudicative decisions performed at the service centers, and manages all other immigration benefits functions but they DO NOT have any duty for immigration enforcement. http://www.USCIS.gov
On the other hand, Immigration and Customs Enforcement (ICE), which is also a component of the Department of Homeland Security is the division that enforces the laws related to the I-9 form.
As of recently, ICE has intensified their review of the current processes. The requirements need to comply with the process of the electronic software and electronic systems that are used by employers for employees to complete the I-9 form electronically. In recent audits from ICE, at employer sites, assessed penalties based on the interpretation of the applicable regulations that the current electronic systems deem to violate the requirements of that require employers to verify and prove the electronic I-9 form was actually "signed" by the employee.
As a result, ICE has made some changes to their requirements for electronic systems. In addition, the USCIS has changed the requirements of the I-9 format.
We have outlined specific changes of the new requirements for both the completion and retention of the I-9 form and the completion of electronic signatures.
These changes are initially intended to simplify the process of completing this form however; this may not be reality. We want to prepare you for what you need to do to be compliant. These small changes, can amount to large fines. For example, fines from audits have ranged from $216 to $2156.00 per each I-9 violation. We're here to help you avoid that from happening.
Some tips on how the hardcopy and the electronic version differ:
Form I-9 Regardless if you're a Trump supporter or otherwise, despite the talk we've been hearing to "Make America Great Again" and the unrealistic promise to build "an impenetrable physical wall on the southern border" of the United States, realistically we know that people with diverse backgrounds will continue to come into this country. Further, they will be hired as employees. With this as our reality, employers must continue to comply with the Immigration Reform and Control Act of 1986, verifying employment eligibility by properly and timely by completing an I-9 for each and every employee.
These changes are initially intended to simplify the process of completing this form however; this may not be reality. We want to prepare you for what you need to do to be compliant. These small changes, can amount to large fines. For example, fines from audits have ranged from $216 to $2156.00 per each I-9 violation. We're here to help you avoid that from happening. An overview of the changes made:
Electronic Version of Form I-9
For instance, employers and employees leaving blank items that must be completed. For example, when completed electronically, the revised Form I-9 detects information that is not entered correctly or is incomplete.
The English version of the electronic form also provides helpful drop-down lists, details about the requested information, and calendars to facilitate accurate completion.
Back to paragraph 4 above, the current electronic systems do not offer a way for the employee to sign the I-9 form, so how do they sign it? We asked the same question. We found the answer on the Department of Homeland Security website.
"Employers who wish to implement an electronic Form I-9 with an electronic signature function may re-create a Form I-9 that includes such a function, as long as the resulting form is legible; there is no change to the name, content, or sequence of the data elements and instructions; no additional data elements or language are inserted; and the standards specified under 8 CFR 274a.2(e) through (i), as applicable, are met. The system used to generate and store the electronic Form I-9 also must comply with regulations found at 8 CFR 274a.2 (e)-(i)." Click here to read more How can I add an electronic signature field to Form I-9?
Instructions for Form I-9
FYI – The instructions for the revised form went from seven pages to a ballooned 15 pages. Key things to remember:
First and foremost this has not changed, unfortunately too many employers do it. Employers are not allowed to tell employees which documents to use. If you do this, please STOP.
The instructions are now encompassed in a separate document
Employers using paper versions of the Form I-9 are now required to make these instructions available, either in paper format or electronically, during the completion of the form.
"Preparer and/or Translator Certification" is now a supplement to the I-9, on a separate third page. For employers using paper forms, this will increase the likelihood of the certification becoming separated from the remainder of the form.
SECTION 1. Translator or Preparer
Must now have a "yes" or "no"
Additionally, the revised I-9 now requires employees to affirmatively indicate whether they used a translator or preparer to complete Section 1, and to check "no" if they did not do so. In the past if an employee did not use a translator, the section was left blank.
SECTION 2. Additional Information Box
The revised form now has a box in Section 2 for "additional information."
Examples of what the employer might include there are noted on the electronic version of the form. However, items that cannot be added in this section are:
Employment authorization extensions,
Additional documents that cannot be entered in the drop-down boxes:
E-Verify case numbers
Employee termination dates
Form retention dates
SECTION 3. Does not have any changes
Remember employers, particularly those using the paper version of the Form I-9, should be cautious not to include in the "additional information" box or on the form additional documentation provided by the employee beyond those legally permitted and other extraneous and potentially inappropriate information. And employers should keep in mind that anything appearing in that box will be available to USCIS in the course of any later audit.
Governmental Compliance Audits
Typical audits uncover 85 to 90 percent error rates; with most of the issues being technical errors that can be corrected before the government comes knocking on the company's door.
ICE gives the company only 72 hours to provide the requested documentation.
Changes to be prepared for July 1, 2017.


Mobile network operator, Econet Wireless, has announced plans to give Harare First Street a major facelift which will see the company repaving pavements and designing clean family-friendly sitting areas with water features, children's play area, translucent seats, benches, open air theatre sitting and solar phone charging ports.
Econet, which is partnering Harare City Council, also plans to redo the First Street Police Post by deploying an eco-friendly and energy efficient container with air-conditioning, surveillance monitoring screens with split view, patrol self-balancing electric scooters, coffee and water dispensers.
Speaking at a breakfast meeting with stakeholders to launch the regeneration of the First Street Mall, the company's chief of staff, Mr Lovemore Nyatsine, said they had experts who will work with the city council in different aspects of the development and no budget has been set for the programme which can be implemented in phases.
"Smart street lighting with closed circuit television will be the first step towards the development of smart city as this increases the energy efficiency of the city, reduce energy costs, reduce carbon emissions, reduce maintenance costs, enhance public safety and improve traffic control," he said.
Other features on Econet plans include street lights information booth surveillance system digital screens, Wi-Fi information booth, surveillance system, digital screens, Wi-Fi, police post pavements and kerbs sitting areas, landscaping and vending kiosks toilets bins.
Smart solar-powered digital sign boards designed to serve as a stand-alone information-sharing platform with e-ink displays will also be erected.
Self-service kiosks will also be erected to allow payment of rates and water bills, as well as purchase of electricity tokens.
Econet also wants modern digital billboards in the form of solar-powered digital screens with live streaming capabilities for displaying paid adverts, specialised messages such as birthday wishes, weather forecast, breaking news and major sporting events.
Harare mayor Councillor Herbert Gomba said it was time to bid farewell to the Harare of the past and welcome the new vision of a smart city.
"We want a city that competes with world capitals in terms of infrastructure, architecture, service delivery and facilities," he said. "Our central business district has deteriorated and is no longer attractive. Buildings are in bad shape, they have not been repainted and spruced up in a long time.


essica Hische is my new typography hero. If you haven't already heard, she is putting out a new dropcap every work day that you can use on your noncommercial blog for free! This print was hand done by her on a letterpress and is the first set of drop caps that she did.


text:
Q: Ruby on Rails - prepopulate new record I have a form for a nested resource (Client :has_many Workouts) that I want to pre-populate based on some user input (I use this input to set up some other default parameters for the new action).
<%  form_tag new_client_workout_path(@workout_user) do%>
    <%= date_select nil, :date %>
    <%= submit_tag 'Enter New Workout' %><br/>
<% end %>

If I submit this form I get the following error.
ActionController::MethodNotAllowed Only get, put, and delete requests are allowed.

I can update the form's method to get, which works, but then I have all of my form paramters on the query string which I don't want.
Is there some way to accomplish this using a post?
I've done something similar when the resource wasn't nested and it worked fine.

A: So, as I understand it, you want a form (as shown) to be sent as a POST to a controller which causes another form to be rendered which is pre-populated with date-directed parameters (from the first form), right?
It's unconventional but you could just change the new action of your WorkoutsController so accept a POST instead of the conventional GET. In routes.rb
map.resources :clients do |clients|
  clients.resources :workouts, :new => { :new => :post }
end

UPDATE
The clean RESTful way to do something like this is to have a separate controller (working title - ConfigWorkoutsContoller) and actions (new and create) for the first form as follows;

*

*ConfigWorkoutsContoller#new renders the form (as shown) which is a GET

*Its submit action is a POST to the create action with the date

*ConfigWorkoutsContoller#create pre-populates a @workout instance and renders WorkoutsController#new

A: I'm not sure if this is directly related to your issue, but when using nested resources, you need to pass both resources to your form tag for it generate the proper routes. Meaning:
<%  form_tag new_client_workout_path(@client, @workout) do %>

I don't know enough about the specifics of what you are doing, so it's a little tough to get you to the answer directly. What is @workout_user? What do your routes look like?
Edit:
After seeing your reply below, the "cleaner way" to do this would be to do:
<%  form_tag(new_client_workout_path(@workout_user), :method => :get) do %>

Note: the guides seem to use a quoted "get", but I think a symbol works as well.

A: I was able to get it to work by adding a hidden form field
<%= hidden_field_tag '_method', 'get' %>

so that the form method is post, but the rest method is get
Not sure if I'm doing all this the right way or if there is a more accepted way of getting user input to the new action.  Normally, you would get all your user input from the new action, but in this case I'm building the form differently depending on what date the user selects.

redpajama_set_name: RedPajamaStackExchange


How your baby's name sounds when it is said aloud is one of the most essential things to think about.
Often, longer first names work better with shorter last names, and vice versa.
It may be best to avoid first names that rhyme with your surname, too. And it's also probably wise to resist puns. A name like "Holly Wood" or "Rosie Lee" will be fun for about five minutes, not a lifetime.
An unusual name has the advantage of making the bearer stand out from the crowd. BabyCenter mum Soraya sometimes wishes she hadn't chosen the popular name Adam for her second son. When he started school, there were three other Adams in his class, which meant that he lost a little of his individuality.
On the other hand, a name no one has heard of and can't pronounce can draw unwanted attention. One way of striking a balance is to choose a familiar first name if your child's surname is unusual. But if your son's surname will be Chan, you may want to consider something with more pizzazz for his first name.
Many parents choose to name their babies after a grandparent, relative, or close friend. This option can provide you with a good pool of names to consider. Take ideas graciously, but don't tell anyone what you and your husband have decided until after your baby is born. This means that it will be too late for you to give in to any less-than-subtle hints.
Never let anyone pressure you into choosing a name you don't like. When it comes down to it, great aunt Hepzebiah won't have to live with the name, your baby will.
Your child's heritage is an essential part of who she is, and you may want her name to reflect that. Your religion could steer you towards a certain category of names. Or perhaps your family has a tradition of naming first-born sons after their fathers. If you love a name but it doesn't meet your family's traditional requirements, consider using it as a middle name.
No one is likely to treat your daughter Ingrid differently because her name means "hero's daughter", but the derivation of your baby's name is something you may want to think about. After all, if little Stockard finds out one day that her name means "from the yard of tree stumps", she may not be best pleased.
People, especially children, can be cruel when it comes to nicknames, so try to anticipate any potentially embarrassing ones. Of course, just because you don't think of something doesn't mean some clever classmate down the line won't - and he'll probably find it utterly hilarious. But at least you can rule out the obvious problems.
Also, be aware of what your child's initials spell. Zachary Ian Thomas will more than likely get a lot of teasing, while Zachary Edward Thomas probably won't.
Remember, none of these are hard-and-fast rules. The most important criteria for a name is simply that you and your husband like it.
Try out our baby name finder.
You could also discuss baby names with other parents-to-be in our Pregnancy forum today.
I've found out that I'm carrying twins. How can I give them suitable names?


text:
Ontario Heritage Trust presents Lieutenant Governor's Ontario Heritage Awards Français
Ontario Heritage Trust
TORONTO, Feb. 27, 2015 /CNW/ - Today, the Ontario Heritage Trust, in partnership with the Office of the Lieutenant Governor of Ontario, announced the recipients of the Lieutenant Governor's Ontario Heritage Awards, recognizing individuals and groups who have made outstanding contributions to conserving Ontario's heritage.
Individuals, groups, and communities are recognized for demonstrating leadership, commitment, creativity, positive impact on their community and good conservation practices. The 2014 winners of the Lieutenant Governor's Ontario Heritage Awards are:
Youth achievement - individual / Young Heritage Leaders scholarship
Mélanie-Rose Frappier (Sudbury)
Muhammad Qureshi (Mississauga)
Youth achievement - group
Huzza for Freedom: Political Cartoons and the War of 1812 Exhibit (Toronto)
Juno Beach Project (Smiths Falls, Oakville and Owen Sound)
Métis Nation of Ontario Canoe Expedition (province wide project)
Bill Darfler (Brantford)
George Gordon (Oakville)
Wayne Hunter (Brantford)
Susan Laing (Clarington)
William Marks (Bradford West Gwillimbury)
Patricia Rosebrugh (Waterloo)
Allan Smith (Grimsby)
Barbara Weese (Greater Napanee)
Excellence in Conservation
The City of Barrie and E.R.A. Architects Inc. for restoration of Allandale CNR Station
John and Josefa Dunstall for the restoration of Grimsby Old Firehall
The City of Mississauga, ATA Architects Inc. and Baker Turner Inc. for the rehabilitation of Holcim Waterfront Estate
Town of Grimsby
Great-West Life, London Life and Canada Life have supported the Young Heritage Leaders program since its inception with funding through the companies' national corporate citizenship program. The recipients of the Young Heritage Leaders scholarship will be presented with a $2,000 post-secondary scholarship, jointly funded by the Ontario Heritage Trust and Great-West Life, London Life and Canada Life.
"On behalf of the people of Ontario, I want to thank and congratulate everyone honoured today for their exemplary achievements in conserving our province's heritage. Our precious natural landscapes and cultural treasures define who we are and what we value. It is through the dedication, excellence and innovation of individuals and communities such as these that Ontario's heritage will continue to be celebrated and enjoyed by future generations."
— The Honourable Elizabeth Dowdeswell, Lieutenant Governor of Ontario
"Our province has a rich and diverse heritage and I'm proud of our government's ongoing commitment to preserve it. The efforts of those individuals, communities and organizations being recognized with a 2014 Lieutenant Governor's Ontario Heritage Award deserve our praise and hopefully inspire more Ontarians to follow their lead. Congratulations to all those being honoured and thank you for your hard work."
— The Honourable Michael Coteau, Minister of Tourism, Culture and Sport
"Each year, we take this opportunity to celebrate exceptional contributions to conserving Ontario's rich cultural and natural heritage. These remarkable individuals have demonstrated creativity, leadership and excellence. Their commitment to preserving Ontario's tangible and intangible heritage deserves our highest praise."
— Thomas H.B. Symons, Chairman of the Ontario Heritage Trust
"We've supported the Ontario Heritage Trust's youth program for over a decade because it encourages young people to serve in their communities, preserving local heritage, protecting the environment and demonstrating excellence. Our shared goal is to empower and inspire young leaders to greater involvement and commitment to build strong, vibrant and diverse communities for the future."
— Jan Belanger, Vice-President, Community Relations, Great-West Life, London Life and Canada Life
Find out about the award winners in the 2014 Lieutenant Governor's Ontario Heritage Award backgrounder.
Visit www.heritagetrust.on.ca/recognition for information about the Trust's recognition program, including how to submit a nomination.
The Ontario Heritage Trust is an agency of the Government of Ontario dedicated to identifying, preserving, protecting and promoting Ontario's heritage.
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www.heritagetrust.on.ca
www.facebook.com/ontarioheritagetrust
www.twitter.com/ONheritage
www.youtube.com/HeritageOntario
SOURCE Ontario Heritage Trust
For further information: For more information about the Trust's recognition program, contact Catrina Colme at 416-325-5074 or [email protected]; For more information about Great-West Life, London Life and Canada Life, contact Marlene Klassen, Assistant Vice-President, Communication Services, at 204-946-7705 or [email protected]
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