A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

The Level of Knowledge, Behaviors, and Attitudes on Rational Use of Drugs of Patients Who Applied to the Family Health Center in Istanbul, Türkiye: A Cross-Sectional Study

Background: This study, it was aimed to determine the level of knowledge, attitudes, and behaviors of patients who applied to a family health center about the rational use of drugs. Irrational use of drugs is a major problem worldwide. WHO reports that half of the patients do not use their drugs correctly. Methods: This cross-sectional study was conducted between 1 October 2017 and 30 November 2018 at Istanbul Fatih Family Health Center No 7. The sample size was determined as 301 people selected by systematic sampling method from patients aged 18 and older. Results: The mean age of the participants was 53.8% ± 16.8%, 59.8% were female, 62.5% were married, and 52.5% were primary school graduates. 63.9% of the participants knew the names of the drugs they used, and 79.9% of them knew the indication for use. 89% of individuals check the expiry date of the drugs before using them, and 83.1% read the drug prospectus. 84% of the participants support the prohibition of using over-the-counter drugs. Conclusion: The level of knowledge of the participants about the rational use of drugs is above the societal average. However, some issues need more awareness. The high level of rational use of drugs awareness of physicians and pharmacists will also strengthen the rational use of drugs and indirectly increase the awareness of the public.

ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ（; E0, E） is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ（Ω; E0, E） to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.

Effect of Luteolin on Biochemical,Immunohistochemical,and Morphometrical Changes in Rat Spinal Cord following Exposure to a 900 MHz Electromagnetic Field

Objective This study aimed to investigate the effect of exposure to a 900 MHz electromagnetic field(EMF)on the cervical spinal cord(CSC)of rats and the possible protective effect of luteolin(LUT)against CSC tissue damage.Methods Quantitative data were obtained via stereological,biochemical,immunohistochemical,and histopathological techniques.We investigated morphometric value,superoxide dismutase(SOD)level,and the expression of high-mobility group box 1 protein molecules,as well as histological changes.Results The total number of motor neurons in the EMF group significantly decreased in comparison with that in the control group(P<0.05).In the EMF+LUT group,we found a significant increase in the total number of motor neurons compared with that in the EMF group(P<0.05).SOD enzyme activity in the EMF group significantly increased in comparison with that in the control group(P<0.05).By contrast,the EMF+LUT group exhibited a decrease in SOD level compared with the EMF group(P<0.05).Conclusion Our results suggested that exposure to EMF could be deleterious to CSC tissues.Furthermore,the protective efficacy of LUT against SC damage might have resulted from the alleviation of oxidative stress caused by EMF.

Some Universal Properties of the Green’s Functions Associated with the Wave Equation in Bounded Partially-Homogeneous Domains and Their Use in Acoustic Tomography

Direct and inverse scattering problems connected with the wave equation in non-homogeneous bounded domains constitute challenging actual subjects for both mathematicians and engineers. Among them one can mention, for example, inverse source problems in seismology, nondestructive archeological probing, mine prospecting, inverse initial-value problems in acoustic tomography, etc. In spite of its crucial importance, almost all of the available rigorous investigations concern the case of unbounded simple domains such as layered planar or cylindrical or spherical structures. The main reason for the lack of the works related to non-homogeneous bounded structures is the extreme complexity of the explicit expressions of the Green’s functions. The aim of the present work consists in discovering some universal properties of the Green’s functions in question, which reduce enormously the difficulties arising in various applications. The universality mentioned here means that the properties are not depend on the geometrical and physical properties of the configuration. To this end one considers first the case when the domain is partially-homogeneous. Then the results are generalized to the most general case. To show the importance of the universal properties in question, they are applied to an inverse initial-value problem connected with photo-acoustic tomography.

Logarithmic Sine and Cosine Transforms and Their Applications to Boundary-Value Problems Connected with Sectionally-Harmonic Functions

Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.

Matrix Functions of Exponential Order

Both the theoretical and practical investigations of various dynamical systems need to extend the definitions of various functions defined on the real axis to the set of matrices. To this end one uses mainly three methods which are based on 1) the Jordan canonical forms, 2) the polynomial interpolation, and 3) the Cauchy integral formula. All these methods give the same result, say g(A), when they are applicable to given function g(t) and matrix A. But, unfortunately, each of them puts certain restrictions on g(t) and/or A, and needs tedious computations to find explicit exact expressions when the eigen-values of A are not simple. The aim of the present paper is to give an alternate method which is more logical, simple and applicable to all functions (continuous or discontinuous) of exponential order. It is based on the two-sided Laplace transform and analytical continuation concepts, and gives the result as a linear combination of certain n matrices determined only through A. Here n stands for the order of A. The coefficients taking place in the combination in question are given through the analytical continuation of g(t) (and its derivatives if A has multiple eigen-values) to the set of eigen-values of A (numerical computation of inverse transforms is not needed). Some illustrative examples show the effectiveness of the method.

How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?

We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3=Constant, where P isthe pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work （Yarman et al. 2010 Int. J. Phys. Sci. 5 1524）. We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.

Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra

We investigate the inhomogeneous invariance quantum group of the d-dimensional d-parameter deformed boson algebra.It is found that the homogeneous part of this quantum group is given by the𝑑-parameter deformed general linear group.We construct the d-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case.

A Contemporary Research on Reality of Armenian Genocide and the Countermeasures Organization With Management

Today,half the world,almost all of the most developed countries and Western countries,formally recognizes the Armenian Genocide.In certain states of the USA and in some European countries,such as Switzerland,saying that“the genocide isn’t real”or even arguing about it is considered an offence will get you into prison.This is a behavior that does not comply with the moral code of the hypocritical West,which has been applying double standards for centuries.The Turks have faced the one-sided,brutal,and unrealistic accusations and oppression of the West for five centuries,and the same type of irrational impositions by both the USA and the European Union still continue to this day.The Turkish people are unprepared against the Armenian claims.The blind admiration to the West,the lack of foresight on the part of the leaders,and unfortunately the unresponsiveness of the Turkish society have always encouraged the West.This state of affairs should be stopped as soon as possible.

Hans Morgenthau’s Lack of Definition of National Power in the 21st Century:Intelligence

Power is a constantly discussed phenomenon in international relations.In this direction,the definition of“power”has been interpreted differently from past to present.Among these definitions,the theory of realism explained the complex and dynamic international system in the simplest way,especially according to the conditions of the Cold War period.The theory of realism has often helped guide government policy.It also indicated the issues that states should focus on.During the Cold War period,especially the neo-realist approach of Hans Morgenthau,the element of national power formed an important guide for the characteristic policies of states.The elements of national power,which Hans Morgentha diversifies as political uncertainty,economic doubt,science and technology,demography,geography,military as a whole,are all internationally wide-ranging.However,it gives an incomplete answer to the international system of the 21st century.In the 21st century,states have increased their focus on intelligence.Many states,especially America,have examined the intelligence scientifically.Today,it is accepted as a scientific field.The study tries to explain that the lack of Hans Morgenthau’s understanding of power is“intelligence”.

Embedding Theorems in J5-Spaces and Applications

This study focuses on the anisotropic Besov-Lions type spaces Bp,θl(Ω; E0, E) associated with Banach spaces E0 and E. Under certain conditions, depending on l = (l1,l2,…,ln) andα= (α1,α2,…,αn), the most regular class of interpolation space Eαbetween E0 and E are found so that the mixed differential operators Dαare bounded and compact from Bp,θl+s(Ω;E0,E) to Bp,θs (Ω; Eα). These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties.

Compact embedding in Besov spaces and B-separable elleptic operators

Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are two Banach spaces and E 0 E.The most regular class of interpolation space E α,between E 0 and E are found such that the mixed differential operator D α is bounded and compact from B p,q l,s (Ω;E 0,E) to B p,q s (Ω;E α) and Ehrling-Nirenberg-Gagliardo type sharp estimates established.By using these results the separability of differential operators with variable coefficients and the maximal B-regularity of parabolic Cauchy problem are obtained.In applications,the infinite systems of the elliptic partial differential equations and parabolic Cauchy problems are studied.

Carleman estimates and unique continuation property for the anisotropic differential-operator equations

The unique continuation theorems for the anisotropic partial differential-operator equations with variable coeffcients in Banach-valued Lp-spaces are studied.To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations,the suffcient conditions are founded.By using these facts,the unique continuation properties are established.In the application part,the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.

Free Boundary Value Problems for Abstract Elliptic Equations and Applications

The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.