期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2021; 131 (2)
Varying-coefficient time series model has gained wide attention because of its flexibility and interpretability. This article considers the single-ind......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2021; 131 (1)
Marks (J. Algebra280 (2004) 463-471) proved that if the skew polynomial ring R[x;sigma] is left or right duo, then R[x;sigma] is commutative. It is pr......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2021; 131 (1)
Let G be a finite group. A vanishing element of G is an element g is an element of G such that chi (g)=0 for some irreducible complex character chi of......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
Suppose that the finite group G = AB is a mutually permutable product of two p-soluble subgroups A and B. By using the Wielandt lenghts of Sylow p-sub......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
Let C be a triangulated category with shift functor [1] and R a contravariantly rigid subcategory of C. We show that a tilting subcategory of mod R li......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
Let G = (V, E) be a graph. A subset S subset of V is a 2-dominating set of G if each vertex in V - S is adjacent to at least two vertices in S. The 2-......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
In 2011, Sun (Sci. China Math. 54 (2011) 2509-2535) made the following conjecture: for any odd prime p and odd integer m, 1/m(2)((m-1) ((m-1)/2)) (Sig......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
In this paper, we establish the weak laws of large numbers for the negative quadrant-dependent random sequences which extend the classic Kolmogorov-Fe......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
A composite number is a positive integer that has at least one divisor integer other than 1 and itself. In this paper, we give a detailed structural d......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
In this article, we investigate the sign changes of the sequence of coefficients at sum of two squares where the coefficients are the Fourier coeffici......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
Let R(n) denote the number of representations of an even integer n as the sum of two squares, two cubes and two sixth powers of primes, and by E(N) we......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
In an earlier work, we proved a generalized entropy ergodic theorem for finite nonhomogeneous Markov chains (NMC). In this paper, we establish a gener......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
For positive integers d and n, the vector space H-d (x(1), x(2), ..., x(n)) of homogeneous polynomials of degree d is a representation of the symmetri......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
We consider the inequality | pc1 + pc2 + pc3 - N| < (log N)- E, where 1 < c < 281 250, N is a sufficiently large real number and E > 0 is ......
期刊： PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2020; 130 (1)
In this paper, we recall some well known Berger's formulas. As their applications, we prove that if the local holomorphic pinching constant is. < 2......
