The Analysis on the Relationship between Dating and the Gel-ink Material Penetration of Handwriting along Z Direction on Paper

Scanning electron microscopy (SEM) technology has been widely used in forensic science, which promotes the development of interdisciplinary science. This paper used SEM to observe the penetration degree of common black gel-ink on paper. The penetration morphology of the different black brands gel-ink has been observed. The relationship between the penetration process of gel-ink material and the dating of document has been observed after determining the measuring position. The results showed that the penetration depth of ink along Z direction on paper is significantly different, the penetration speed of ink is also different, which presents regular variety and gradually reaches a relatively stable state over time. The application of SEM will provide a useful exploration for judging the ink dating.

Optical properties of Einstein–Born–Infeld gravastar models in plasmas

Gravastar models have recently been proposed as an alternative to black holes, mainly to avoid the problematic issues associated with event horizons and singularities. Recently, in [D. J. Cirilo-Lombardo and C. D. Vigh, Int. J. Mod. Phys. D 28 (2019) 1950108], a regular variety of gravastar models within the context of Einstein–Born–Infeld (EBI) nonlinear electrodynamics were built. These original models are truly regular in the sense that both the metric and its derivatives are continuous throughout spacetime, contrary to other cases in the literature where matching conditions are necessary in the interior and exterior regions of the event horizon. In this work, in the same theoretical context from [D. J. Cirilo-Lombardo and C. D. Vigh, Int. J. Mod. Phys. D 28 (2019) 1950108], we study some optical phenomena, such as the weak gravitational lens for the case of the magnetized plasma and the influence of working with a nonlinear field of BI in observables such as the Einstein ring or the total delay time. These important issues allow us to compare the results obtained in the context of these new static Born–Infeld gravastars with the standard linear ones (e.g. Reissner–Nordström).

TATE’S CONJECTURE AND THE TATE–SHAFAREVICH GROUP OVER GLOBAL FUNCTION FIELDS

Let ${\mathcal{X}}$ be a regular variety, flat and proper over a complete regular curve over a finite field such that the generic fiber $X$ is smooth and geometrically connected. We prove that the Brauer group of ${\mathcal{X}}$ is finite if and only Tate’s conjecture for divisors on $X$ holds and the Tate–Shafarevich group of the Albanese variety of $X$ is finite, generalizing a theorem of Artin and Grothendieck for surfaces to arbitrary relative dimension. We also give a formula relating the orders of the group under the assumption that they are finite, generalizing the known formula for a surface.

Einstein–Born–Infeld gravastar models, dark matter and accretion mechanisms

Gravastar models have recently been proposed as an alternative to black holes, mainly to avoid the problematic issues associated with event horizons and singularities. In this work, a regular variety of gravastar models within the context of Einstein–Born–Infeld (EBI) nonlinear electrodynamics are builded. These models presented here are truly regular in the sense that both the metric and its derivatives are continuous throughout spacetime, contrary to other cases in the literature where matching conditions are necessary in the interior and exterior regions of the event horizon. We investigated the accretion process for spherically symmetric spacetime geometries generated for a nonlinear electromagnetic field where the energy–momentum tensor has the same form that an anisotropic fluid that is the general EBI case. We analyze this procedure using the most general static spherically symmetric metric ansatz. In this theoretical context, we examined the accretion process for specific spherically symmetric compact configuration obtaining the accretion rates and the accretion velocities during the process and the flow of the fluid around the black hole. In addition, we study the behavior of the rate of change of the mass for each chosen metric.

Study of Availability, Pattern of consumption and Proximate Principles of Ready to Eat Packaged Diet and Regular Snacks, in the city of Mumbai

The present study on the availability, pattern of consumption and proximate principles of Ready to eat packaged (RTEP), Regular and Diet snacks was conducted in the city of Mumbai. 36 Shopkeepers and 100 consumers from different areas of Mumbai were interviewed as per semi-structured questionnaire specifically designed for this study. Shopkeepers were asked about the availability, shelf life and sale of RTEP regular and Diet snacks. Consumers were also individually interviewed about their dietary patterns and their preference of regular and diet RTEP snacks. Fives type of frequently consumed RTEP snacks (Khakhara, Chivada, Chakri, Wafers (Banana) and Biscuits (Khari)) (regular and their diet variety) were selected and 250 grams of each of them were coded and given for analysis of proximate principles to an ISO-9000 certified laboratory. It was observed that a wide variety of RTEP Diet snacks are available in the city of Mumbai. RTEP diet snacks are perceived as more expensive by shopkeepers and consumers. Chivada, Khakara and Biscuits (Khari) are most widely consumed regular and diet snacks. Consumption of Diet RTEP snacks depends on age, gender, religion and the family income of the consumer. Only RTEP Diet Khakhra comply with the standards and are a good option for those who wish to consume less calorie and fat in their meals. Other RTEP Diet snacks do not have less than 3 grams of fat per serving. Caution should be taken as salt content in Diet Khakhra, Chivada and Chakri is more by 52%, 10% & 136% respectively than their regular variety.

BERNSTEIN–SATO POLYNOMIALS AND TEST MODULES IN POSITIVE CHARACTERISTIC

In analogy with the complex analytic case, Mustaţă constructed (a family of) Bernstein–Sato polynomials for the structure sheaf${\mathcal{O}}_{X}$and a hypersurface$(f=0)$in$X$, where$X$is a regular variety over an$F$-finite field of positive characteristic (see Mustaţă,Bernstein–Sato polynomials in positive characteristic, J. Algebra321(1) (2009), 128–151). He shows that the suitably interpreted zeros of his Bernstein–Sato polynomials correspond to the$F$-jumping numbers of the test ideal filtration${\it\tau}(X,f^{t})$. In the present paper we generalize Mustaţă’s construction replacing${\mathcal{O}}_{X}$by an arbitrary$F$-regular Cartier module$M$on$X$and show an analogous correspondence of the zeros of our Bernstein–Sato polynomials with the jumping numbers of the associated filtration of test modules${\it\tau}(M,f^{t})$provided that$f$is a nonzero divisor on$M$.

Performance of Eight Varieties of Onion (Allium cepa L.) Cultivated under Open Field in Tunisia

A field experiment was conducted from September 2010 to July 2011 at Research Station Farm of Higher Institute of Agronomy, Chott Mariem, Sousse (Tunisia) in order to evaluate the performance of seven onion varieties: ‘GIZA 6’, ‘Red Amposta’, ‘Z6’, ‘Morada de Amposta’, ‘Yellow Dessex’, ‘Early Yellow Texas Grano 502’ and ‘Keep Red’ against the commonly grown variety ‘Blanc Hâtif de Paris’ under field conditions. The experiment was conducted in a randomized complete block design with three replications. Results obtained showed that onion varieties were significantly different when it comes to the plant and bulb morphological characteristics. Variety ‘Morada de Amposta’ recorded the highest leaf length (68.06 cm), pseudostem diameter (8.63 cm), number of leaves (8.71), plant height (76.95 cm), in addition to the greatest yields (32.88 t/ha) which were significantly (p≤0.05) increased by respectively 66.2, 88.8, 2.1, 61.2, 63, 27.9 and 28.4% compared to those obtained from the regular variety ‘Blanc Hâtif de Paris’. Variety ‘Blanc Hâtif de Paris’ was the earliest to maturity and recorded the most preferment bulb weight (155.02 g) and diameter (8.21 cm). ‘Keep Red’ variety had the highest height of the bulb (7.19 cm). Variety ‘Z6’ recorded the minimum data in all measured parameters.

A language for all the world

In the popular mind, constructing a language has always been seen as an odd activity, one that seems to fly in the face of ‘natural’ language dynamics. It is, nonetheless, a very old activity, and attention to its various stages is an important part of the study of linguistic history – and, indeed, of modern scientific development. The first stage involves attempts (highly speculative, of course) to recapture the original lingua humana, as spoken in the Garden of Eden. At a later stage, scholars tried to create entire languages ab ovo, motivated by the desire for a more logical and regular variety that would better reflect and channel scientific classification. Later still – and on into the modern era – ‘artificial’ languages have been assembled from pre-existing rules and components. At all stages, the work has been underpinned by hopes for a more practical medium, but there have also been expectations that a language that was both regular and widely shared would contribute to international harmony and understanding.

Quasi-subtractive varieties

Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras. Abstract algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety the lattice of congruences of A is isomorphic to the lattice of deductive filters on A of the τ-assertional logic of . Moreover, if has a constant 1 in its type and is 1-subtractive, the deductive filters on A ∈ of the 1-assertional logic of coincide with the -ideals of A in the sense of Gumm and Ursini, for which we have a manageable concept of ideal generation.However, there are isomorphism theorems, for example, in the theories of residuated lattices, pseudointerior algebras and quasi-MV algebras that cannot be subsumed by these general results. The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ-regularity in such a way as to shed some light on the deep reason behind such theorems. The tools and concepts we develop hereby provide a common umbrella for the algebraic investigation of several families of logics, including substructural logics, modal logics, quantum logics, and logics of constructive mathematics.