Indian Journal of Pure and Applied Mathematics最新文献

In this paper, it is proved that with at most (O(N^{frac{13}{96}+varepsilon })) exceptions, every sufficiently large even integer satisfying (nleqslant N), (nnot equiv 2,(textrm{mod},3)) can be represented as the sum of two squares of primes, one cube of primes and three biquadrates of primes. This result constitutes a refinement upon that of the author [6].

In this paper, our goal is to establish novel inequalities for the Euclidean operator radius of a pair of bounded linear operators defined on a complex Hilbert space. Additionally, we use the Heilbronn inequality to derive further inequalities relevant to both single and pairs of Hilbert space operators.

In this work, we considered a Singular Perturbation Problem (SPP) with an integral boundary condition. Two numerical methods, namely Variable Mesh Spline Approximation Method (VMSAM) and Cubic B-Spline Collocation Method (CBSCM) are discussed to obtain second order convergence in the supremum norm. Numerical examples are presented to validate the obtained results.

The study of unimodular rows over a commutative ring involves the utilization of Suslin matrices. These matrices possess a Fundamental Property, which plays a crucial role in establishing connections between the group generated by special Suslin matrices and the special orthogonal group. Moreover, the Fundamental Property serves as a means to establish a link between Suslin matrices and Spin groups. In this work, we focus on (2 times n) row Suslin matrices, defining them and exploring their properties. We provide a proof for the Fundamental Property specific to (2 times n) row Suslin matrices.

We first make an approach to the Mittag-Leffler condition in the theory of relative Ext-orthogonal classes and establish the balance of the relative derived functors of the Hom and tensor product functors with respect to the classes of projectively coresolved Gorenstein flat modules and Gorenstein injective modules. Then, we introduce the concepts of PGF-tilting modules and PGF-weak tilting modules. By means of Mittag-Leffler conditions, we explore the connection between PGF-tilting modules and PGF-weak tilting modules. As an application, we study when Gorenstein tilting modules are Gorenstein weak tilting.

The cone-disk system, featuring a cone in contact with a disk at its apex, is a versatile arrangement used in applications such as conical diffusers, viscosimeters and medical devices. Present research focus on the theoretical analysis of gold blood nanofluid flow in cone disk system for Tiwari and Das model in the presence of thermal radiation. The three dimensional axisymmetric gold blood nanofluid flow is analysed for four distinct models namely model I (rotating cone and static disk), model II (static cone and rotating disk), model III (co-rotating cone and disk) and model IV (counter rotating cone and disk). The governing non-linear equations are transformed to self similar equations by using one parameter Lie group approach and solved by using bvp5c package of MATLAB to examine the effect of different parameters involving in the problem. In order to validate the result, Nusselt number at cone and disk surfaces are compared with the published literature and the closed agreement authenticates the validation of the problem. The influence of various parameters on velocity and temperature profile of gold blood nanofluid has been discussed in detail for all four configurations of cone disk system for the gap angle (frac{pi }{4}) and are shown graphically. The result of this analysis shows that there is a outward radial flow as a result of high centrifugal forces due to rotation of disk/cone. Also the velocity of nanofluid decrease with increasing the nanoparticle volume fraction. The results also reveal that an increase in the nanoparticle volume fraction, power exponent, and radiation parameter values leads to an increase in the temperature profile.

Parthasarathy’s heritage has a hidden component arising from a variant of his concept of shift-compactness which yields quick proofs of fundamental theorems reviewed here. We demonstrate the closeness of the variant notion to his original one as arising in the tacit treatment of all possible convergent centrings. We also include a very short proof of the Effros Mapping Theorem – a non-linear version of the Open Mapping Theorem. This is deduced from a shift-compactness theorem. Both these can be given a constructive form by implementing a constructive improvement to a theorem on the separation of points and closed nowhere dense sets.

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate Whitney numbers of the second kind associated with Y and the probabilistic fully degenerate Dowling polynomials associated with Y, which are the probabilistic versions of the degenerate Whitney numbers of the second kind and the fully degenerate Dowling polynomials. We derive generating functions, some properties, explicit expressions, certain identities, recurrence relations for those numbers and polynomials.

In this paper, we introduce new classes of rings, namely, (n^{*})-nil clean ring, (sum )-nil clean ring and BB-ring, and we study the possible transfer of the notions of (n^{*})-nil clean ring, (sum )-nil clean ring, k-good ring, nil-good ring and BB-ring to various context of commutative ring extensions such as homomorphic image, direct product, power series ring and amalgamation ring, with applications to the transfer of these properties in trivial ring extension. Our work is motivated by an attempt to generate new original classes of rings possessing these properties.

In this paper, we study the existence of bounded solutions for a nonlinear anisotropic parabolic equation with degenerate coercivity and a singular term on the right-hand side. The model problem considered is as follows

where (Omega ) is a bounded open subset of (mathbb {R}^{N}) (Nge 2), (T>0), (2le p_{i}<N) for every (i=1,ldots ,N), (theta ,gamma ge 0), (0le fin L^{m}(Q)) with (m>frac{N}{overline{p}}+1) ((overline{p}) defined in (2.1)) and (Q=Omega times (0,T)). The main idea in the proof is based on Stampacchia’s lemma, which allows us to obtain a priori estimates by making a suitable choice of a test function.