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Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely P ∗ (n) , M (n) , T ∗ (n) , L (n) , K (n) , A (n) , and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo 2 a · 5 ℓ for P ∗ (n) , modulo 2 3 for M(n) and T ∗ (n) , where a = 3 , 4 and ℓ ≥ 1 . For instance, we prove that for n ≥ 0 , P ∗ (5 ℓ (4 n + 3) + 5 ℓ - 1) ≡ 0 (mod 2 3 · 5 ℓ). In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: M (5 n + 4) ≡ 0 (mod 5) , T ∗ (5 n + 3) ≡ 0 (mod 5). [ABSTRACT FROM AUTHOR]

This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for α ∈ (0 , 1) is established with the help of the α -resolvent kernel and the Schauder-fixed point theorem. The non-continuation theorem is proved by the fixed point technique and accordingly the global existence of solution is achieved. The uniqueness of the solution is obtained using the contraction principle and the stability results are discussed by means of Ulam-Hyers and generalized Ulam-Hyers-Rassias stability concepts via the Picard operator. Examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold: first, we obtain various curvature inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Kenmotsu space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion. The equality cases of all the inequalities are studied. Moreover, these curvature inequalities are studied under two different cases: the structure vector field ξ being vertical or horizontal. [ABSTRACT FROM AUTHOR]

This paper investigates some well-posedness issues of the fractional inhomogeneous Schrödinger equation i u ˙ - (- Δ) γ u = ± | x | ρ | u | p - 1 u , where 0 < γ < 1 and ρ < 0 . Here, one considers the inter-critical regime 0 < s c : = N 2 - 2 γ + ρ p - 1 < γ , where s c is the energy critical exponent, which is the only one real number satisfying ‖ κ 2 γ + ρ p - 1 u 0 (κ ·) ‖ H ˙ s c = ‖ u 0 ‖ H ˙ s c . In order to avoid a loss of regularity in Strichartz estimates, one assumes that the datum is spherically symmetric. First, using a sharp Gagliardo–Nirenberg-type estimate, one develops a local theory in the space H ˙ γ ∩ H ˙ s c . Then, one investigates the L N (p - 1) ρ + 2 γ concentration of finite-time blow-up solutions bounded in H ˙ s c . Finally, one proves the existence of non-global solutions with negative energy. Since one considers the homogeneous Sobolev space H ˙ s c , the main difficulty here is to avoid the mass conservation law. [ABSTRACT FROM AUTHOR]

In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing ∗ -hermicity over complex field. The compact formula of the general solution of this system is presented in terms of generalized inverses when some necessary and sufficient conditions are fulfilled. An algorithm and a numerical example are provided to validate our findings. A numerical example is carried out using determinantal representations of the Moore–Penrose inverse. [ABSTRACT FROM AUTHOR]

In the present paper, we consider a special class of third-order polynomial evolutionary equations. These equations, via Lie theory admit the same one-parameter point transformations which leave the equations invariant. Reductions with these invariant functions lead to highly nonlinear third-order ordinary differential equations. We use a power series to establish interesting solutions to the reduced equations, whereby recurrence relations occur and convergence of the series may be tested. Finally, the conserved vectors of the class are constructed. [ABSTRACT FROM AUTHOR]

In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]

The notion of approximate fixed point sequence, emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool in proving convergence theorems for fixed point iterative schemes in the class of nonexpansive-type mappings. In the present paper, our aim is to present simple and unified alternative proofs of some classical fixed point theorems emerging from Banach contraction principle, by using a technique based on the concepts of approximate fixed point sequence and graphic contraction. [ABSTRACT FROM AUTHOR]

In this paper, we will prove some fixed point theorems for graphical contractions in complete b-metric spaces. Then, some common fixed point results for a pair of mappings in complete b-metric spaces will be deduced. Our results extend some recent theorems proved in classical metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, two new estimators E 2 k - 1 , 0 (1) (f) and E 2 k - 1 , M (1) (f) of characteristic function and an estimator E 2 k - 1 , M (2) (f) of function of H o ¨ lder's class H α [ 0 , 1) of order 0 < α ⩽ 1 have been established using Bernoulli wavelets. A new technique has been applied for solving Volterra integral equation of second kind using Bernoulli wavelet operational matrix of integration as well as product operational matrix. These matrices have been utilized to reduce the Volterra integral equation into a system of algebraic equations, which are easily solvable. Some examples are illustrated to show the validity and efficiency of proposed technique of this research paper. [ABSTRACT FROM AUTHOR]

This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a (P , η) -accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(.,.)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms K s (ε) . We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of ξ . Moreover, we acquire Chen-Ricci inequalities on the ker ϑ ∗ and (ker ϑ ∗) ⊥ distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of ξ . [ABSTRACT FROM AUTHOR]

Of concern is a Cohen–Grossberg neural network (CGNNs) system taking into account distributed and discrete delays. The class of delay kernels ensuring exponential stability existing in the previous papers is enlarged to an extended class of functions guaranteeing more general types of stability. The exponential and polynomial (or power type) type stabilities becomes particular cases of our result. This is achieved using appropriate Lyapunov-type functionals and the characteristics of the considered class. [ABSTRACT FROM AUTHOR]

This paper deals with some existence and uniqueness results for a class of deformable fractional differential equations. These problems encompassed nonlinear implicit fractional differential equations involving boundary conditions and various types of delays, including finite, infinite, and state-dependent delays. Our approach to proving the existence and uniqueness of solutions relied on the application of the Banach contraction principle and Schauder's fixed-point theorem. In the last section, we provide different examples to illustrate our obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlocal elliptic problem involving a mixed local and nonlocal operator, (P) ∫ Ω f (x , u) d x β L p , s (u) = f α (x , u) in Ω , u > 0 in Ω , u = 0 in R N \ Ω , where Ω ⊂ R N is a bounded regular domain, L p , s ≡ - Δ p + (- Δ) p s , 0 < s < 1 < p < N , α , β ∈ R and f : Ω × R → R be a nonnegative function which is defined almost everywhere with respect to the variable x. Using Schauder and Tychonoff fixed point theorems, we get two existence theorems of weak positive solutions under some hypothesis on α , β and f. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system's dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems. [ABSTRACT FROM AUTHOR]

In this paper, we study the current T ∧ dd c ψ for positive currents T and semi-exhaustive, not necessarily plurisubharmonic, functions ψ . The study leads to new definitions of capacity and Lelong–Demailly numbers with respect to the weight ψ . [ABSTRACT FROM AUTHOR]

In this paper, we prove that any group occurs as the group of homotopy classes of self-equivalences of a none elliptic Sullivan algebra. [ABSTRACT FROM AUTHOR]

This paper presents several properties and relations that satisfy the components of a bicomplex holomorphic function. It also exhibits several analogies and differences with the case of analytic functions. [ABSTRACT FROM AUTHOR]

In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry analysis as part of our approach together with some number theoretic functions. Our findings generalize certain results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the heat transfer modeling during freezing of a biological tissue and present an analytical approach for solving the heat transfer problem in cryosurgery. We consider a time-fractional bio-heat equation in the cylindrical coordinate and employ the Wiener–Hopf technique to find the temperature of tissue in two different domains by the factorization of associated Wiener–Hopf kernel. We discuss the fundamental roles of the Bessel and Wright functions in determining the analytical solution of fractional cryosurgery problem. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo fractional derivatives with initial and integral conditions. Some new results on the existence and uniqueness of a solution for the model are obtained as well as the Ulam stability of the solutions. Two examples are provided to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a coupled system of hyperbolic and biharmonic-wave equations with variable exponents in the damping and coupling terms. In each equation, the damping term is modulated by a time-dependent coefficient a(t) (or b(t)). First, we state and prove a well-posedness theorem of global weak solutions, by exploiting Galerkin's method and some compactness arguments. Then, using the multiplier method, we establish the decay rates of the solution energy, under suitable assumptions on the time-dependent coefficients and the range of the variable exponents. We end our work with some illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider a weighted fractional stochastic integro-differential equation with infinite delay and nonzero initial values involving a Riemann–Liouville fractional derivative of order 1 / 2 < α < 1 . The existence of a mild solution is investigated using fractional calculus, stochastic analysis, and the fixed point theorem. An example is also provided to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for nonlinear equations called the reaction–diffusion model. Using only three properties, this analysis provides convergence results for several conforming and non-conforming numerical schemes that align with the GDM. As an application of this analysis, the hybrid mimetic mixed (HMM) method for the reaction–diffusion model is designed, and its convergence is established. Numerical experiments using the HMM method are presented to facilitate the study of the creation of spiral waves in the Barkley model and the ways in which the waves behave when interacting with the boundaries of their generating medium. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a class of impulsive nonlinear evolution partial differential equations. We give new results about existence and multiplicity of global classical solutions. The method used is based on the use of fixed points for the sum of two operators. Our main results will be illustrated by an application to an impulsive Burgers equation. [ABSTRACT FROM AUTHOR]

In this paper, we will focus on following nonlocal quasilinear elliptic system with singular nonlinearities: (S) (- Δ) p s 1 u = 1 v α 1 + v β 1 in Ω , (- Δ) q s 2 u = 1 u α 2 + u β 2 in Ω , u , v = 0 in (I R N \ Ω) , u , v > 0 in Ω , where Ω ⊂ I R N be a smooth bounded domain, s 1 , s 2 ∈ (0 , 1) , α 1 , α 2 , β 1 , β 2 are suitable positive constants, (- Δ) p s 1 and (- Δ) q s 2 are the fractional p - Laplacian and q - Laplacian operators. Using approximating arguments, Rabinowitz bifurcation Theorem, and fractional Hardy inequality, we are able to show the existence of positive solution to the above system. [ABSTRACT FROM AUTHOR]

Given a nonempty convex subset X of a topological vector space and a real bifunction f defined on X × X , the associated equilibrium problem consists in finding a point x 0 ∈ X such that f (x 0 , y) ≥ 0 , for all y ∈ X . A standard condition in equilibrium problems is that the values of f to be nonnegative on the diagonal of X × X . In this paper, we deal with equilibrium problems in which this condition is missing. For this purpose, we will need to consider, besides the function f, another one g : X × X → R , the two bifunctions being linked by a certain compatibility condition. Applications to variational inequality problems, quasiequilibrium problems and vector equilibrium problems are given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iteration process, called multi-valued F-iteration process, for the approximation of fixed points. We introduce a new class of multi-valued generalized nonexpansive mappings satisfying a B γ , μ property. Moreover, we establish certain weak and strong convergence theorems in uniformly convex Banach spaces. We also discuss the stability of the modified F-iteration process. Furthermore, a numerical example is presented to illustrate the superiority of our results. [ABSTRACT FROM AUTHOR]

The parallelogram law characterizes a part of the structure of Hilbert spaces. To hold the parallelogram law by the norm, reasonably good conditions are required for Banach spaces. This paper proposes new type parallelogram laws with bifunctions on Banach spaces and geodesic spaces, respectively. [ABSTRACT FROM AUTHOR]

Speedy advancement in research in Astrophysics and related area around the globe has led scientists in Central Asia to produce high-quality research and constitute strong research in Relativistic Astrophysics and the Einstein theory of gravitation. Consequently, immense impact of this progress has been seen in central Asian countries in not only in research in Astrophysics and related areas, the academic institutions also received a trickle down effect in terms of the advancement in teaching as well as research. This focus of this paper is to overview the research incentives that are being taken up by the Theoretical Astrophysics Group located at Ulug Beg Astronomical Institute of Uzbekistan Academy of Sciences, Tashkent. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the possible ways of distinguishing regular and singular black holes (BHs) in modified gravity (MOG) called regular MOG (RMOG) and Schwarzschild MOG (SMOG) BHs through observational data from twin peak quasiperiodic oscillations (QPOs) which are generated by test particles in stable orbits around the BHs. The presence of MOG field causes to sufficiently the mpeak in effective potential for a radial motion of test particles. The effect of MOG parameter on specific angular momentum and energy has also studied. As a main part of the paper, we focus on investigations of QPOs around SMOG and RMOG BHs in RP model and the relations of upper and lower frequencies of twin peak QPOs in SMOG and RMOG BH models together with extreme rotating Kerr and Schwarzschild BH. Moreover, possible parameters for the central BHs of the objects GRS J1915 + 105 and XTE 1550 – 564 have also obtained numerically in the relativistic precession (RP) model. Finally, we provide comparisons of the innermost stable circular orbit (ISCO) and the orbits where twin peak QPOs with the ratio 3:2 taken place and show that QPOs can not be generated at/inside ISCO and there is a correlation between the radius of ISCO and QPO orbits. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the decay properties of the thermoelastic suspension bridges model. We prove that the energy is decaying exponentially. To our knowledge, our result is new and our method of proof is based on the energy method to build the appropriate Lyapunov functional. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study the notion of quasi-bi-slant submanifolds of almost contact metric manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant, and quasi-hemi-slant submanifolds. We study and characterize quasi-bi-slant submanifolds of Sasakian manifolds and provide non-trivial examples to signify that the structure presented in this paper is valid. Furthermore, the integrability of distributions and geometry of foliations are researched. Moreover, we characterize quasi-bi-slant submanifolds with parallel canonical structures. [ABSTRACT FROM AUTHOR]

In this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of σ -filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a σ -filtered skew PBW extension A over a ring R is a graded skew PBW extension over the homogenization of R. Using this fact, we prove that if the homogenization of R is Auslander-regular, then the homogenization of A is a domain Noetherian, Artin–Schelter regular, and A is Noetherian, Zariski and (ungraded) skew Calabi–Yau. [ABSTRACT FROM AUTHOR]

This paper is devoted to examine necessary and sufficient conditions for a Frenet curve to be f-harmonic, f-biharmonic, bi-f-harmonic and f-biminimal in three-dimensional β -Kenmotsu manifolds. In addition, such conditions are investigated for slant curves. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to examine the isometries of almost Ricci–Yamabe solitons. Firstly, the conditions under which a compact gradient almost Ricci–Yamabe soliton is isometric to Euclidean sphere S n (r) are obtained. Moreover, we have shown that the potential f of a compact gradient almost Ricci–Yamabe soliton agrees with the Hodge–de Rham potential h. Next, we studied complete gradient almost Ricci–Yamabe soliton with α ≠ 0 and non-trivial conformal vector field with non-negative scalar curvature and proved that it is either isometric to Euclidean space E n or Euclidean sphere S n. Also, solenoidal and torse-forming vector fields are considered. Lastly, some non-trivial examples are constructed to verify the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study the stabilization problem of a disk beam structure with disturbance. Specifically, the structure consists of a beam clamped at one end to the center of a rotating rigid disk, while the other end is attached to a tip mass subject to a non-uniform bounded disturbance. We start the investigation by designing the controller via the Active disturbance rejection control (ADRC) approach. The high gain extended state observer (ESO) is first designed to estimate the disturbance, then the feedback observer-based controller is designed to employ the estimation to cancel the disturbance effect. Furthermore, the well-posedeness of the controlled system is proved using the semigroup theory. Using the Lyapunov method, the exponential stability is proved. Finally, the performance of the control method is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, approximate Noether and Lie symmetries of 2nd order for Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) charged black hole in the Einstein frame are analyzed comprehensively. To explore the approximate Noether symmetries of 2nd order, Noether symmetries of Minkowski spacetime are used which forms a 17 dimensional Lie algebra. It is observed that no new approximate Noether symmetry is obtained at 1st and 2nd order. To examine the 1st and 2nd order approximate Lie symmetries of the GMGHS black hole spacetime, 35 Lie symmetries (exact) of the Minkowski spacetime are used which forms an algebra sl(6, R). It is shown that no new approximate Lie symmetry exists at 1st and 2nd order and only exact 35 symmetries are recouped as trivial approximate Lie symmetries at both orders. Furthermore, no energy rescaling factor is seen in this spacetime. [ABSTRACT FROM AUTHOR]