In this work, a mathematical analysis of a time-dependent coupled system of convection-diffusion-reaction equations with mixed Dirichlet and Neumann boundary conditions that arise in fluidized bed spray granulation is investigated. The system serves as a representation of the temperature and concentration distributions within a fluidized bed. This work establishes the existence and uniqueness of a weak solution for the model equations with linear reaction terms, relying on classical findings. Employing these outcomes in conjunction with Schauder’s fixed point theorem, the work further demonstrates the existence and uniqueness of a solution for the model equations featuring nonlinear reaction terms.
In a Lipschitz domain Ω⊂ℝ^N , we investigate the boundary behavior of positive superharmonic functions u satisfying the nonlinear inequality -Δ u(x)≤ cd(x,∂Ω )^-τu(x)^p . Based on the fact that, in some ranges of p and τ , the possible growth rate of u near ∂Ω is given by the reciprocal of d(x,∂Ω )^N - 2 g_Ω (x) using the Green function g_Ω with a fixed pole, we estimate the size of a set of points in ∂Ω where a nontangential limit superior of d(x,∂Ω )^N-2-β g_Ω (x)u(x) diverges for a given β≥ 0 .
In this paper, we provide two sufficient conditions, in terms of the horizontal gradient of two horizontal velocity components and the gradient of magnetization field, for the breakdown of local-in-time strong solutions to the three-dimensional incompressible Navier–Stokes-Landau-Lifshitz system with Dzyaloshinskii-Moriya interaction and a V-flow term. We prove that if T_* is the maximal existence time of the local strong solution (u, d) and T_* < +∞ , then ∫ _0^T_*( ‖∇ _h u^h ‖ _Ḃ^0_p,2p/3^q + ‖∇ d ‖ _Ḃ^0_∞ ,∞^2 ) dt = ∞ with 3/p + 2/q = 2, 3/2 < p ≤∞ , or ∫ _0^T_*( ‖∇ _h u^h ‖ _Ḟ^0_p,2p/3^q + ‖∇ d ‖ _Ḟ^0_∞ ,∞^2 ) dt = ∞ with 3/p + 2/q = 2, 3/2 < p ≤∞ , where ∇ _h = (∂ _1, ∂ _2) and u^h = (u^1, u^2) denote the horizontal gradient and the horizontal velocity components, respectively.
In this paper, we introduce inner product preserving homomorphisms and strong norm preserving homomorphisms in Hilbert C^* -modules and adopt the fixed point method to prove their Hyers–Ulam stability.
Time delay effects and memory-driven dynamics are known to be included in a delay partial differential equation. A physics-consistent extension of Newton’s second law, the neutral delay formulation synchronizes modeling with real-world measurement techniques. Neutral delay time space distributed order fractional damped diffusion wave equations are typically too complex to solve analytically, necessitating the use of numerical techniques. The neutral delay time–space distributed order fractional damped diffusion wave equation is solved in this study using a time–space Jacobi pseudospectral quadrature simulation method. The Riesz fractional derivative sense is used to characterize the fractional derivatives. The suggested approach for discretizing spatial domains is based on Jacobi–Gauss–Lobatto collocation points, which make it easier to integrate the resultant algebraic equation system across time. Newton’s method is then used to solve the system. The error analysis for the suggested numerical approach is also provided. Finally, several numerical tests are shown to demonstrate the excellent approximation and high accuracy of the suggested approach.
We consider a class of multi-valued operators T:X→ P(X) having the property that there exists an admissible perturbation of it, defined as T_G:X→ P(X) and satisfying a Ćirić type contraction condition. This work focuses on the conditions imposed on the admissible perturbation T_G , such that strict fixed point results hold true for T. The main result consists of formulating a theorem that connects the properties of the admissible perturbation with the conclusion that T is a Picard operator. Additionally, we study whether the strict fixed point problem T(x)={x} is well-posed, as well as, data dependence, Ulam-Hyers stability and Ostrowski property for the strict fixed point problem. The admissible perturbations in the sense of Takahashi serve as a relevant example for applying the theory formulated in this paper.
This article examines a family of Liénard systems possessing four singular points in the finite plane, classified as 2A + 2S (two antisaddles and two saddles). Improved methods are presented for constructing such systems with a prescribed number of limit cycles, including cycles that enclose a group of singular points. A conjecture regarding the conditions for the absence of such enclosing cycles is proposed, and a sufficient condition of their absence is proved. The study introduces algorithms for generating predictive bifurcation curves, which partition the space of damping coefficients into domains characterized by a fixed distribution of limit cycles. The methodology is illustrated on two quartic restoring forces; for each of them the full list of realizable distributions is obtained, and representative distributions, including the mixed one ((1, 1), 1), are confirmed by direct numerical integration.
A three-layered structure, comprising functionally graded piezoelectric materials positioned between a hard-dielectric layer and an elastic half-space, is analyzed to investigate the propagation characteristics of shear-horizontal (SH) waves. The top surface is assumed to be stress-free and subjected to electrical short boundary conditions, while the interfaces are modeled as welded contacts. Solutions are obtained via variable-separation methods, which transform the governing partial differential equations (PDEs) into a system of ordinary differential equations (ODEs) that are then solved using standard techniques. The resulting dispersion relation is obtained under the specified boundary conditions. For demonstration, a specific model is examined. Graphs depicting phase velocity as a function of wavenumber are presented to elucidate the numerical results.
In this paper, we study sectional structures embedded in the t-scaled hypercomplex numbers ℍ_t for a scale t∈ℝ . For a fixed scale t∈ℝ , from the subset 𝕊_t consisting of a certain type of pure-imaginary t-scaled hypercomplex numbers in ℍ_t , we sectionize ℍ_t . We concentrate on such a section 𝕊ℍ_I_t for an arbitrarily fixed imaginary I_t∈𝕊_t , called the t-sliced section for I_t . We construct some functional vector spaces induced by 𝕊ℍ_I_t over the real field ℝ , and concentrate on one of the vector space SH_I_t:2[ [ q] ] called the 𝕊ℍ_I_t -Hardy space. An interesting type of operators on SH_I_t:2[ [ q] ] is introduced and studied. Especially, we are interested in Toeplitz-like operators. Operator algebra, operator theory, and certain noncommutative-statistical data induced by such Toeplitz-like operators are characterized and analyzed.
In the present paper, we introduce the Hausdorff-type operators associated with the multidimensional Hankel-type Segal–Bargmann transform ℬ_α ; and we prove the boundedness of these operators on the space L^2(μ _α) . We give a relation between the multidimensional Hankel-type Segal–Bargmann transform and the Hankel-type Hausdorff operators. We investigate multidimensional Hankel-type localization operators, and obtain some useful results. The relation between multidimensional Hankel-type localization operators and Hankel-type Hausdorff operators is also established. The results of this paper are illustrated by some known examples.
We prove a Peano–Sard type representation theorem for continuous linear functionals involving 1st level general fractional derivatives of arbitrary order defined via Sonin kernels. Under a natural null–space condition, such functionals admit an integral representation in terms of an associated Peano kernel and the 1st level general fractional derivative of arbitrary order. This framework unifies and extends classical results for Riemann–Liouville, Caputo, and Hilfer fractional derivatives. As an application, we establish a new sharp lower bound for the L^2 –norm of the 1st level general fractional derivative and characterize the extremal functions. Examples with power–law kernels illustrate the results and recover known inequalities as special cases.
One of the main aims of the present paper is to study some inequalities for semi-Hilbertian space operators involving A-numerical radius and A -operator seminorm, which generalize and improve some classical numerical radius inequalities for complex Hilbert space operators.
This article is devoted to the study of a two–parameter special function, namely the Krätzel function, which is widely recognized in applied analysis. The work aims to contribute new and significant results to the existing literature on the Krätzel function. In particular, a series representation is derived using an unconventional method, called the method of brackets. Furthermore, matrix–variate extensions of the Krätzel function are developed in both real and complex domains. The closed–form representation of the Krätzel function of matrix argument has been achieved via Fox’s H–function of matrix arguments using M–transform techniques. Furthermore, it has been proved that the matrix–variate fractional maps such as Riemann–Liouville, Erdélyi–Kober and Weyl operators are compatible with the proposed Krätzel function of matrix arguments in both real and complex domains. These results broaden the theoretical foundation of the Krätzel function and enhance its potential applicability in multivariate and matrix–variate analysis.
This work proposes a memory-based dynamic event-triggered control (DETC) scheme for the dissipativity analysis of polynomial fuzzy systems (PFS) operating under Denial-of-Service (DoS) attacks. The PFS model incorporates additive time-varying delays (ATVDs) to ensure robustness and maintain stability in practical settings where delays are inherently uncertain. To enhance adaptability and retain reliable performance, a memory-based DETC mechanism is designed to effectively suppress the adverse effects of DoS attacks. A suitably constructed Lyapunov-Krasovskii functional (LKF), enriched with integral terms, is employed to accurately capture the influence of ATVDs. Using parameter-dependent reciprocal convex inequalities (RCIs), tractable sufficient conditions are derived and formulated as sum-of-squares (SOS) constraints. Numerical simulations validate the proposed approach, demonstrating its effectiveness and potential for real-world implementation.
A normalized analytic function f in the open unit disk 𝔻 is called a Bloch function if it satisfies sup _z ∈𝔻 (1 - |z|^2) |f'(z)| ≤ 1 . The function f is Ma–Minda starlike (or convex) with respect to φ if zf'(z)/f(z) (or 1+zf”(z)/f'(z) ) maps 𝔻 into φ (𝔻) . In this paper, we determine the Ma–Minda radii of starlikeness and convexity for several choices of φ , whose image domains φ (∂𝔻) include the exponential domain ( φ (z)=e^z ), a cardioid domain ( φ (z)=1+(4z)/3+(2z^2)/3 ), the lune region generated by ( φ (z)=z+√(1+z^2) ), a shifted cardioid domain associated with a rational function ( φ (z)=1+ ((z^2+kz)/(k^2-kz)) ) where k=√(2)+1 , a special case of a contracted cardioid domain ( φ (z)=1+ze^z ), another cardioid domain ( φ (z)=1+z+z^2/2 ), and the limacon cardioid–type domain ( φ (z)=(1+z/√(2))^2 ). In addition, lower bounds for the radii are obtained when φ maps ∂𝔻 onto classical geometric regions such as the right half–lemniscate domain ( φ (z)=√(1+z) ), the shifted–sine domain ( φ (z)=1+sin z ), the nephroid region ( φ (z)=1+z-z^3/3 ), the sigmoid region ( φ (z)=2/(1+e^-z) ), the three leaf–type domain ( φ (z)=1+(4z)/5+z^4/5 ), the petal–shaped domain ( φ (z)=1+sinh ^-1 z ), and the hyperbolic–cosine convex region ( φ (z)=cosh√(z) ).
This work concerns the study of the exact boundary controllability for some non-densely defined semilinear partial functional differential equations with nonlocal initial conditions, in the framework of general Banach spaces. We establish sufficient conditions for the exact controllability of a class of non-densely defined boundary control problem. We do this by using the theory of integrated semigroup and the measure of noncompactness. The existence of solutions is achieved by using the Mönch fixed point theorem without assumming compactness of the C_0 -semigroup on the closure of the domain. As a result, we obtain a generalization of several important results in the literature. An example is given to illustrate the applicability of our abstract results.
The increasing prevalence of adulterated food has been linked to a range of health problems in humans. In response, the consumption of organic food has grown due to its perceived health benefits. This study proposes a novel stochastic eco-epidemiological model to investigate the spread of foodborne diseases in a population that has access to both adulterated and organic food. In the model, food is modeled as a population since its level changes over time due to production and consumption processes. It is treated as prey in the ecological sense, as it is consumed by the human population for survival and nutrition. Humans act as predators in this interaction. Human population is divided into two categories: susceptible and infected individuals. It is assumed that two types of food are available in the market, where disease is induced only by the consumption of adulterated food, while organic food contributes positively to health. The model employs a Holling type II functional response to describe the consumption of adulterated food by the susceptible population. We begin by analyzing the deterministic version of the model, establishing positivity and boundedness of the system. The equilibrium points and their existence conditions are derived, and the local as well as global stability of feasible equilibria are examined. Hopf bifurcation analysis is further carried out to explore the local dynamics near equilibrium states. To incorporate environmental variability, the model is extended into a stochastic framework, where the existence of a unique global positive solution is established. Lyapunov functions are then constructed to investigate the asymptotic stability of the equilibria. Finally, numerical simulations are presented to validate and illustrate the theoretical results.
In the present paper, we will provide both necessary and sufficient conditions ensuring that the sum and product of n-hypo-EP operators remain n-hypo-EP. Moreover, we examine the restrictions of n-hypo-EP operators.
Let 𝒮 denote the class of univalent functions in the unit disk 𝔻:={z∈ℂ:|z|<1} with the form f(z)=z+∑ _n=2^∞a_nz^n . The logarithmic inverse coefficients Γ _n of f∈𝒮 are defined by F_f^-1(w):=log( f^-1(w)/w) =2∑ _n=1^∞Γ _nw^n valid for some disk |w|≤ r_0(f) . The second Hankel determinant of logarithmic inverse coefficients is defined by H_2( 2) ( F_f^-1/2) =Γ _2Γ _4-Γ _3^2. In this paper, we obtain sharp upper bound of the second Hankel determinant H_2( 2) ( F_f^-1/2) of the logarithmic inverse coefficients of starlike and bounded turning functions.
