# Indian Journal of Pure and Applied Mathematics

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 239-252

*H*

^{4}(Ω) when the initial value belongs to

*H*

^{1}(Ω).

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 69-81

*B*

_{1}be an open ball of radius

*r*

_{1}in the complex projective space. Let

*B*

_{0}be a smaller open ball inside it. It is shown that first Dirichlet eigenvalue of the Laplacian on

*B*

_{1}\ $$\overline {{B_0}} $$ B 0 ¯ is maximal if and only if the balls are concentric.

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 213-224

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 149-160

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 191-202

_{b,c}, defined by hypergeometric functions, with the α-logarithmic Bloch spaces

*B*

_{log,α}of analytic functions.

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 113-120

*F*

_{2}+

*uF*

_{2}with

*u*

^{2}= 0. This problem was first proposed by AbuAlrub

*et al*. in (Des Codes Crypt

**42**: 273-287, 2007). Also we extend this decoding procedure for cyclic codes of arbitrary length over the ringe $$\frac{{{F_2}\left[ u \right]}}{{\langle {u^t}\rangle }} = {F_2} + u{F_2} + {u^2}{F_2} + \cdots {u^{t - 1}}{F_2}$$...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 95-112

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 253-268

*r, s*)-even function is a special type of periodic function mod

*r*

^{s}. These functions were defined and studied for the the first time by McCarthy. An important example for such a function is a generalization of Ramanujan sum defined by Cohen. In this paper, we give a detailed analysis of DFT of (

*r, s*)-even functions and use it to prove some interesting results including a generalization of the Hölder...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 225-238

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 269-281

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 283-292

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 203-212

*S*, ω) be a weighted abelian semigroup. We show that a ω-bounded semigroup multiplier on

*S*is a multiplication by a bounded function on the space of ω-bounded generalized semicharacters on

*S*; and discuss a converse. Given a ω-bounded multiplier α on

*S*, we investigate the induced weighted semigroup (

*S*

_{α}; ω

_{α}). We show that the ω

_{α}-bounded generalized semicharacters on

*S*

_{α}are scalar multiples of ω-bounded...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 51-67

*L*

^{1}coefficient matrix satisfying generalized periodic boundary value conditions. And then we will investigate nontrivial solutions for asymptotically linear second-order Hamiltonian systems and obtain some new results.

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 15-22

*Indian J. Pure Appl. Math*.

**48**(2) (2017), 177-185] on the extraction four sequences of orthogonal polynomials from generating function from reciprocal of odd numbers, in this note we identify the weight functions and the intervals of orthogonality of these sequences of polynomials. Two of these sequences can be expressed in terms of particular Jacobi polynomials...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 23-34

*G*= ℤ

_{2}act freely on a finitistic space

*X*with mod 2 cohomology ring isomorphic to the product of a real projective space and 2-sphere $$\mathbb{S}^2$$ S 2 . In this paper, we determine the Conner and Floyd’s mod 2 cohomology index and the Volovikov’s numerical index of

*X*. Using these indices, we discuss the nonexistence of equivariant maps $$X\rightarrow\mathbb{S}^n$$ X → S n ...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 161-169

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 83-94

*K*

_{n}for any positive integer

*n*.

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 171-179

*p*-group by finite dimensional compact connected abelian groups.

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 137-148

*p*

_{{3,3}}(

*n*), the number of 3-regular partitions in 3-colors. We find the generating functions for

*p*

_{{3,3}}(

*n*) and deduce congruences modulo large powers of 3. We also find the generating functions and congruences for linear combination of

*p*

_{3}(

*n*) (the number of partitions of

*n*in 3-colors) by finding the relation connecting

*p*

_{3}(

*n*) and

*p*

_{{3,3}}(

*n*). As an application, we find finite discrete convolution...

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 1 > 121-135