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If (S, ◦,≤) is an ordered hypersemigroup, an equivalence relation ρ on S is called congruence if (a, b) ∈ ρ implies (a ◦ x, b ◦ x) ∈ ρ and (x ◦ a, x ◦ b) ∈ ρ for every x ∈ S ; in the sense that for every u ∈ a ◦ x there exists v ∈ b ◦ x such that (u, v) ∈ ρ and for every u ∈ x◦a there exists v ∈ x◦b such that (u, v) ∈ ρ. It has been proved in Turk J Math 2021(5) [On the paper “A study on (strong) order-congruences in ordered semihypergroups”] that if S is an ordered hypersemigroup, then there exists a congruence ρ on S such that S/ρ is an ordered hypersemigroup. This result, is the main result for an involution ordered hypersemigroup by Xinyang Feng, Jian Tang and Yanfeng Luo in U.P.B. Sci. Bull, Series A, 2018, but its proof is wrong; the correct proof is given in the present paper. Examples illustrate the results. [ABSTRACT FROM AUTHOR]

Throughout the paper in the title by Jian Tang, Yanfeng Luo and Xiangyun Xie in Turk J Math 42 (2018) the following lemma has been used. Lemma: Let (S, *) be a semihypergroup and ρ an equivalence relation on S. Then (i) If ρ is a congruence, then (S/ρ, ⊗) is a semihypergroup with respect to the hyperoperation (a)ρ ⊗ (b)ρ = ... (c)ρ . (ii) If ρ is a strong congruence, then (S/ρ, ⊗) is a semigroup with respect to the operation (a)ρ ⊗ (b)ρ = (c)ρ for all c ∈ a * b. The property (i) of the paper is certainly wrong as ... (c)ρ is a subset of S and not a nonempty subset of S/ρ as it should be. Property (ii) has no sense in the way is written. In addition, according to the authors, as an application of the results of this paper they solved the open problem on ordered semihypergroups given by Davvaz, Corsini and Changphas in European J Combin 44 (2015). The problem is that the above mentioned problem has not been solved in the above mentioned article; we point out the reason, and we solve it in the present paper. Some further related results; also results necessarily for the completeness of the paper are given. Examples illustrate the results. [ABSTRACT FROM AUTHOR]

This note is written to show that the definition of the LA-semihypergroup by V. Amjad, K. Hila and F. Yousafzai "Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 2014" should be corrected and that it is not enough to replace the multiplication "·" of an LA-semigroup by the hyperoperation "ο" to pass from an LA-semigroup to an LA-semihypergroup. The two examples of the paper based on the definition of the LA-semihypergroup are wrong that is a further indication that this definition needs correction. According to the last section of the paper, the paper generalizes the results of an LA-semigroup by M. Akram, N. Yaqoob and M. Khan "On (m, n) -ideals of left almost semigroups, Appl. Math. Sci. (Ruse) 2013" while the paper duplicates, without citation, the section 4 of the paper by W. Khan, F. Yousafzai, W. Guo and M. Khan "On (m, n) -ideals of left almost semigroups, J. Semigroup Theory Appl. 2014" with the usual change of "·" to "ο". [ABSTRACT FROM AUTHOR]

Let ℓ be a Banach sequence space with a monotone norm in which the canonical system (en) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between ℓ -Köthe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Köthe matrices when every continuous linear operator between ℓ -Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between ℓ -Köthe spaces, under a splitting condition, causes the existence of a common basic subspace. [ABSTRACT FROM AUTHOR]

In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0, 1]. By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results. [ABSTRACT FROM AUTHOR]

The present paper deals with the approximation properties of the linear positive operators, including Δh -Gould-Hopper Appell polynomials. We investigate some theorems for convergence of the operators and their approximation degrees with the help of the classical approach, Peetre's K-functional, Lipschitz class and Voronovskajatype theorem. In the last section of the paper, we introduce the Kantorovich form of the operators and examine the approximation degree. [ABSTRACT FROM AUTHOR]

The Randić index (R) and the geometric-arithmetic index (GA) are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randić and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randić and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6. [ABSTRACT FROM AUTHOR]

In this paper, we examine stacky structures in certain Einstein gravity theories. In brief, using the classical formulation of (vacuum) gravity, with vanishing cosmological constant, we first construct the stack of solutions to Einstein field equations on any given fixed manifold. Using a similar approach and setup, we also study Einstein’s gravity on families of manifolds and define another stack encoding this situation. Later on, we focus on the gauge theoretical interpretation of 3D gravity and provide a natural stack associated with that interpretation. Finally, in a particular setup, we give a natural morphism between the two stacks arising from different descriptions of 3D gravity. [ABSTRACT FROM AUTHOR]

This paper addresses the second-order nonlocal dynamic thermistor problem with two-point boundary conditions on time scales. Utilizing the fixed point theorems by Schaefer and Rus, we establish some sufficient conditions for the existence and uniqueness of solutions. Furthermore, we discuss the continuous dependence of solutions and four types of Ulam stability. We provide examples to support the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the permutation properties of the class of trinomials of the form f(x) = x4q+1 + λ1xq+4 + λ2x2q+3 ∈ Fq²[x] where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and sufficient conditions on λ1 and λ2 such that f(x) permutes Fq², where q is odd and q = 22k+1, k ∈ N. [ABSTRACT FROM AUTHOR]

This paper is concerned with the oscillation of solutions to a class of first-order differential equations with variable coefficients and a general delay argument. New oscillation criteria are established, which improve and extend many known results reported in the literature. A couple of illustrative examples are given to show the efficiency of the newly obtained results. In particular, it is shown that our criteria partially fulfill a remaining gap in a recent sharp result by Pituk et al. [31]. [ABSTRACT FROM AUTHOR]

In this paper, we show that in an almost product manifold there exist curves that are slant submanifolds. We characterize these curves and study them in two and three-dimensional locally product manifolds. Finally, we construct curves in a hypersurface of a Kaehler manifold. [ABSTRACT FROM AUTHOR]

In this paper, we study Bernstein-Nikol’skii-Markov type inequalities for arbitrary algebraic polynomials with respect to a weighted Lebesgue space, where the weight functions have some singularities on a given contour. We consider curves which can contain a finite number of exterior and interior corners with power law tangency of the boundary arcs at those points where the weight functions have both zeros and poles of finite order. The estimates are given for the growth of the module of derivatives for algebraic polynomials on the closure of a region bounded by a given curve, depending on the behavior of weight functions, on the property of curve, and on the degree of contact of the boundary arcs, which form zero angles on the boundary. [ABSTRACT FROM AUTHOR]

In this paper, we define a mixed-base number system over a Weyl group Dn, the group of even-signed permutations. We introduce one-to-one correspondence between the positive integers of the set {1, · · ·, 2n-1n!} and elements of this group, after constructing the subexceedant function associated with the group. Thus, the integer representations of all the classical Weyl groups are now completed. Furthermore, we present an inversion statistic on the group Dn by using a decomposition of a positive root system of this reflection group. This inversion statistic is compatible with the length function on the group Dn. Then we derive some combinatorial properties for the inversion statistic. In addition, we prove that the D-major index is equi-distributed with this inversion statistic on Dn. Finally, we propose a public-key cryptosystem based on both the generalized hidden discrete logarithm problem and the integer representation over the group Dn. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the existence and uniqueness of continuous solutions of the following iterative functional differential equation ... By using of Boyd-Wong's fixed point theorem and under suitable conditions, we establish the existence and uniqueness of a continuous solution. [ABSTRACT FROM AUTHOR]

In this paper, we define the ruled surface in terms of the Darboux vector field of an isotropic curve in a complex 3-space, and we study the ruled surface as an elastic strip along the isotropic curve. First of all, we show that elastic strips along isotropic curves that serve critical points of the modified Sadowsky functional are characterized by three Euler-Lagrange equations. As a result, we give two conservation laws to characterize elastic strips of isotropic curves in complex 3-space and explain an isotropic helix in terms of the force vector. Finally, we give some examples to illustrate elastic strips with isotropic curves in a complex 3-space. [ABSTRACT FROM AUTHOR]

For n = 2, let Pn, In, Tn, and Sn be the partial transformation semigroup, symmetric inverse semigroup, (full) transformation semigroup, and symmetric group on the set Xn = {1, . . ., n}, respectively. In this paper, we find the ranks of certain subsemigroups of Pn, In, and Tn consisting of transformations with idempotent complement whose restrictions to the set Xm belong to the (possible) semigroup Sm, Im, Tm, or Pm for 1 = m = n - 1. [ABSTRACT FROM AUTHOR]

In a number of applied problems (immunology, epidemiology, virology, etc.), there is a need to study the dynamics of the trajectories of the compositions of the Lotka-Volterra mappings. In this paper, some variants of these compositions are considered, in particular, the dynamics of the trajectories of the compositions of the Lotka-Volterra mappings acting in a two-dimensional simplex, with transitive tournaments, which can be applied in the study of these processes. Cards of fixed points are constructed for compositions and the characters of fixed points are studied. [ABSTRACT FROM AUTHOR]

In this study M1 (⌈0 (3) (χ-3), M2 (⌈0 (5), χ5) and M3 (Γ0 (7), χ - 7) have been examined and the formulas for the Fourier Coefficients of theta series and the representation number of positive integers by some quadratic forms 3x1² + 3x1x2 + x2², 5(x1² + x1x2 + x1x3 + x14 + x1² + x2x3 + x2x4 + 3² + x3x4) + 2x4², and 7(x1² + x1x2 + x1x3 + x1x4 + x1x5 + x2² + x2x3 + x2x4 + x2x5 + x3² + x3x4 + x3x5 + x4² + x4x5 + x5² + 7 (x1x6 + x2x6 + x3x6 + x4x6) + 3x6², are determined. This work is a correction to a paper of the same title by Ahmet Tekcan [5]. [ABSTRACT FROM AUTHOR]

Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w* -continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem for these operators is investigated. [ABSTRACT FROM AUTHOR]

A ring R is called semiclean if every element of R can be expressed as sum of a periodic element and a unit. In this paper, we introduce a new class of ring, which is the *-version of the semiclean ring, i.e. the *-semiclean ring. A *-ring is *-semiclean if each element is a sum of a *-periodic element and a unit. The term *-semiclean is a stronger notion than semiclean. In this paper, many properties of *-semiclean rings are discussed. It is proved that if p ∈ P(R) such that pRp and (1 - p)R(1 - p) are *-semiclean rings, then R is also a *-semiclean ring. As a result, the matrix ring Mn(R) over a *-semiclean ring is *-semiclean. A characterization that when the group rings RCr and RG are *-semiclean is done, where R is a finite commutative local ring, Cr is a cyclic group of order r, and G is a locally finite abelian group. We have also found sufficient conditions when the group rings RC3, RC4, RQ8, and RQ2n are *-semiclean, where R is a commutative local ring. We have also demonstrated that the group ring Z2D6 is a *-semiclean ring (which is not a *-clean ring). [ABSTRACT FROM AUTHOR]

In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way, we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge problem for this class of surfaces. [ABSTRACT FROM AUTHOR]

For a nonlightlike nondegenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of lightcone framed curves. [ABSTRACT FROM AUTHOR]

Let Xn denote the chain {1, 2, ..., n} under its natural order. We denote the semigroups consisting of all order-preserving transformations and all orientation-preserving transformations on Xn by On and OPn, respectively. We denote by E(U) the set of all idempotents of a subset U of a semigroup S. In this paper, we first determine the cardinalities of ... (1 ≤ r ≤ n) and then, by using these results, we determine the numbers of idempotents in On and OPn by a new method. Let OP-n denote the semigroup of all orientation-preserving and order-decreasing transformations on Xn. Moreover, we determine the cardinalities of OP-n, OP-n,Y = {α ∈ OP-n: fix(α) = Y } for any nonempty subset Y of Xn and OP-n,r = {α ∈ OP-n: |fix(α)| = r} for 1 ≤ r ≤ n. Also, we determine the number of idempotents in OP- n and the number of nilpotents in OP- n. [ABSTRACT FROM AUTHOR]

Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g-) for a locally summable function g(x). [ABSTRACT FROM AUTHOR]

In this paper, we introduce in a braided setting the notion of left module for an invertible 1-cocycle and we prove some categorical equivalences between categories of modules associated to an invertible 1-cocycle and categories of modules associated to Hopf braces. [ABSTRACT FROM AUTHOR]

In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL2(C). In particular, given a finitely generated purely loxodromic free Kleinian group Γ = ⟨ξ1, ξ2,. . ., ξn⟩ for n ≥ 2, we show that |trace2(ξi) - 4| + |trace(ξiξjξ-1i ξ-1j) - 2| ≥ 2 sinh2 (14 log αn) for some ξi and ξj for i ̸= j in Γ provided that certain conditions on the hyperbolic displacements given by ξi, ξj and their length 3 conjugates formed by the generators are satisfied. Above, the constant αn turns out to be the real root strictly larger than (2n-1)2 of a fourth degree integer coefficient polynomial obtained by solving a family of optimization problems via the Karush-Kuhn-Tucker theory. The use of this theory in the context of hyperbolic geometry is another novelty of this work. [ABSTRACT FROM AUTHOR]

This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given. [ABSTRACT FROM AUTHOR]

This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits. [ABSTRACT FROM AUTHOR]

The paper deals with the twisted Sasaki metric on the unit tangent bundle of n-dimensional Riemannian manifold Mn. The main purpose of the research is to find deformations that preserve the existence harmonic left-invariant unit vector fields on 3-dimensional unimodular Lie groups G with the left invariant metric and harmonic maps G → T1G in case of twisted Sasaki metric on the unit tangent bundle. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map Mn → T1Mn are obtained. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map M² → T1M² with respect to some orthonormal frame are obtained. Left-invariant harmonic unit vector fields and harmonic maps G → T1G, where G is a three-dimensional unimodular Lie group with left-invariant metric, using some orthonormal frame are described. Left-invariant harmonic unit vector fields which determine harmonic maps G → T1G, where G is a three-dimensional unimodular Lie group with left-invariant metric in the particular case of twisted Sasaki metric, namely the vertical rescaled metric are classified. [ABSTRACT FROM AUTHOR]

In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. [ABSTRACT FROM AUTHOR]

Let X and Y be compact Hausdorff spaces with Y hyperstonean. In this paper, we prove that if C(X, R) and C(Y, R) are lattice isomorphic then these Banach spaces are linearly isometric, and, consequently, X and Y are homeomorphic, which in turn implies that X is also hyperstonean. Actually, we prove more than what is ann [ABSTRACT FROM AUTHOR]

In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a singular super-critical Trudinger-Moser inequality on a unit ball of Rn, n ≥ 3. For any p > 1, we set λp(B) = inf u∈W0 1,n (B),u̸≡0 ∫ B |∇u| n dx/ ( ∫ B |u| pdx) n/pas an eigenvalue related to the n-Laplacian. Let S be a set of radially symmetric functions. Precisely, if β ≥ 0 and α < (1 + p/n β)n−1+n/pλp(B), then there exists a positive constant ϵ0 such that when λ ≤ 1 + ϵ0,supu∈W 01,n (B)∩S, ∫ B|∇u|ndx−α( ∫ B |u|p|x|pβdx)n/p≤1∫ B |x| pβ(e αn(1+ p/n β)|u| n/n−1− λ ∑k=0 m |αn(1 + p/n β)u n/n−1 |k/k! ) dx is attained, where αn = nω1/(n−1)n−1, ωn−1 is the surface area of the unit ball in Rn . The proof is based on the method of blow-up analysis. The case λ = 0 was studied by Yang-Zhu in [38]. de Figueiredo [11] considered the case p = 2, β ≥ 0, and α = 0 in two dimension. The case λ = 0, p = n, −1 < β < 0, and α = 0 was considered by Adimurthi-Sandeep [1]. Our results extend those of the above cases. [ABSTRACT FROM AUTHOR]

The results on Γ-hypersemigroups are obtained either as corollaries of corresponding results on ⋎e or poesemigroups or on the line of the corresponding results on le-semigroups. It has come to our attention that Theorem 3.22 in [4] cannot be obtained as corollary to Theorem 2.2 of the same paper as for a Γ-hypersemigroup, (P* (M), Γ,⊆) is a ⋎e-semigroup and not an le-semigroup. Also on p. 1850, l. 12 in [4], the "le-semigroup" should be changed to "⋎e-semigroup". In the present paper we prove Theorems 3.26 and 3.28 stated without proof in [4]. On this occasion, some further results are given to emphasize what we say. The results on Γ-hypersemigroups are obtained from the more abstract structure of the poe-semigroups. Further investigation on poe-semigroups and le-semigroups is interesting. [ABSTRACT FROM AUTHOR]

In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed. [ABSTRACT FROM AUTHOR]

The paper presents existence results of (φ, φ) best proximity points for operators that fulfill implicit type inequalities. Classes of mappings endowed with continuity, monotone or monotone-type properties, and which additionally satisfy some adequate inequalities are studied from this point of view. Applications of our results are given with regard to fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the fibonomial sequence spaces ... and ..., and show that these are BKspaces. Also, we prove that these new spaces are linearly isomorphic to ℓp and ℓ∞. Moreover, we determine the α-, β -, γ -duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space ... . [ABSTRACT FROM AUTHOR]

In this paper, using some combinatorial identities and congruences involving q--harmonic numbers, we establish congruences that for any odd prime p and any positive integer α, ... and ... when n is any integer. [ABSTRACT FROM AUTHOR]

In this paper we work on preserving various types of continuity in ideal topological spaces. The accent will be on θ -continuity and weak continuity. We will give their translations in ideal topological spaces. As a consequence of those results, we will prove that every θ -continuous function is continuous if topologies are generated by θ -open sets and we will give an example of a weakly continuous function which is not τ θ -continuous. This will complete the diagram of relations between continuous, τ θ -continuous, θ -continuous, weakly continuous, and faintly continuous functions. [ABSTRACT FROM AUTHOR]

The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed. [ABSTRACT FROM AUTHOR]

This paper presents a generalization of the concepts of partial-A-isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field ([5, 30, 31]). By extending the definition of partial-A-isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left p-partial-A-isometry as a broader class of operators, including partial-A-isometry and left polynomially partial isometry. Some basic properties of a left p-partial-A-isometry are proven, as well as its relation with A-isometry. Several decompositions of a left p-partial-A-isometry are developed. We consider spectral properties and matrix representation of left p-partial-A-isometries. Additionally, we provide some applications of left p-partial- A-isometries. [ABSTRACT FROM AUTHOR]

In this paper, generalized Pell graphs Πn,k, k ≥ 2, are introduced. The special case of k = 2 are the Pell graphs Πn defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of Πn,k and the generating function of its cube polynomial are determined. The center of Πn,k is explicitly described; if k is even, then it induces the Fibonacci cube Γn . It is also shown that Πn,k is a median graph, and that Πn,k embeds into a Fibonacci cube. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem for the 3D incompressible axisymmetric Hall-MHD system with horizontal velocity dissipation and vertical magnetic diffusion. We obtain a unique global smooth solution of which in the cylindrical coordinate system the swirl velocity fields, the radial and the vertical components of the magnetic fields are trivial. This type of solution has been studied for the MHD system in [17], [16] and [15] and for the Hall-MHD system with total dissipation and diffusion in [11]. Some new and fine estimates are obtained in this paper to overcome the difficulties raised from the Hall term and the loss of vertical velocity dissipation and horizontal magnetic diffusion. Finally we can show that the estimates ... and ... are finite in a priori way and hence obtain the global well-posedness to the system under considered. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse nodal problem for a quadratic pencil of the Sturm -- Liouville equations with parameter-dependent Bitsadze -- Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points. [ABSTRACT FROM AUTHOR]

In this paper, the comparison of finite difference and Fourier spectral numerical methods for an inverse problem of simultaneously determining an unknown coefficient in a parabolic equation with the usual initial and boundary conditions is proposed. We represent the detailed description of the methods and their algorithms. The research work conducted in this paper shows that the Fourier spectral method is highly accurate. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the semigroup On,p of all order-preserving full transformations α on an n-elements chain Xn, where p ∈ Xn is the only fixed point of α. The nilpotent semigroup On,p was first studied by Ayik et al. in 2011. Moreover, On,1 is the maximal nilpotent subsemigroup of the Catalan Monoid Cn. Its rank is the difference of the (n - 1) th and the (n - 2) th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup On,p. We will calculate the rank of On,p for p > 1 and provide a semigroup presentation for On,1. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate various formulas, identities and relations involving Apostol type numbers and parametric type polynomials. By using generating functions and their functional equations, we give many relations among the certain family of combinatorial numbers, the Vieta polynomials, the two-parametric types of the Apostol-Euler polynomials, the Apostol-Bernoulli polynomials, the Apostol-Genocchi polynomials, the Fibonacci and Lucas numbers, the Chebyshev polynomials, and other special numbers and polynomials. Moreover, we give some formulas related to trigonometric functions, special numbers and special polynomials. Finally, some remarks and observations on the results of this paper are given. [ABSTRACT FROM AUTHOR]

In this paper, we aim to present a new and unified way, including the previously mentioned solution methods, to overcome the problem in [7] for closed and bounded valued F -contraction mappings. We also want to obtain a real generalization of fixed point results existing in the literature by using best proximity point theory. Further, considering the strong relationship between homotopy theory and various branches of mathematics such as category theory, topological spaces, and Hamiltonian manifolds in quantum mechanics, our objective is to present an application to homotopy theory of our best proximity point results obtained in the paper. In this sense, we first introduce a new family, which is larger than F* that has often been used to give a positive answer to the problem. Then, we prove some best proximity point results for the new kind of F -contractions on quasi metric spaces via the new family. Additionally, we show that the note given by Almeida et al. [4] is not valid for our results. Therefore, our results are real generalizations of fixed point results in the literature. Moreover, we give comparative examples to demonstrate that our results unify and generalize some well-known results in the literature. As an application, we show that each homotopic mapping to f satisfying all the hypotheses of our best proximity point result has also a best proximity point. [ABSTRACT FROM AUTHOR]

The onset of magnetoconvection (known as Rayleigh-Bénard-Chandrasekhar convection) in two relaxation time viscoelastic liquids is studied here without seeking explicit recourse to a normal stress formulation as is usually done in these studies. Magnetoconvection refers to the flow of fluid in the presence of both thermal gradients (Rayleigh-Bénard convection) and a magnetic field. When these two effects are combined, they can lead to interesting and complex patterns of fluid motion. Understanding magnetoconvection in viscoelastic liquids is crucial for various industrial and scientific applications. The hyperbolic-type of linear momentum equation is decomposed into two first-order equations in time by cleverly separating the viscoelastic effect from the other effects in a clever manner as reported in a recent paper. The results of Maxwell, Rivlin-Ericksen, Walters' liquid B, and Newtonian liquids are obtained as limiting cases of the present study. This research contributes to the understanding of magnetoconvection in viscoelastic liquids by using a novel approach that decouples the viscoelastic effect from other influences. The results obtained shed light on the behaviour of various types of viscoelastic materials and provide valuable insights for practical applications in fields such as materials science, engineering, and geophysics. [ABSTRACT FROM AUTHOR]