scholarly journals On topological properties of spaces obtained by the double band matrix

2017 ◽  
Vol 15 (1) ◽  
pp. 1148-1155
Author(s):  
Suzan Zeren ◽  
Çiğdem Bektaş
Keyword(s):  
Topological Properties ◽  
Band Matrix ◽  
Matrix Mappings

Abstract Let λ denote any one of the spaces ℓ∞ and ℓp and λ(Ť) be the domain of the band matrix Ť. We study ℓp(Ť) for 1 ≤ p ≤ ∞ and give some inclusions and its topological properties. Also, we define the alpha−, beta− and gamma− duals of the space ℓp(Ť). Finally, we give some matrix mappings.

On generalized Fibonacci difference sequence spaces and compact operators

2021 ◽  
pp. 2250116
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Mikail Et
Keyword(s):  
Fractional Order ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Band Matrix ◽  
Matrix Formula ◽  
Necessary And Sufficient ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

In this paper, we introduce Fibonacci backward difference operator [Formula: see text] of fractional order [Formula: see text] by the composition of Fibonacci band matrix [Formula: see text] and difference operator [Formula: see text] of fractional order [Formula: see text] defined by [Formula: see text] and introduce sequence spaces [Formula: see text] and [Formula: see text] We present some topological properties, obtain Schauder basis and determine [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the spaces [Formula: see text] and [Formula: see text] We characterize certain classes of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to any of the space [Formula: see text] [Formula: see text] [Formula: see text] or [Formula: see text] Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces [Formula: see text] and [Formula: see text]

scholarly journals Sequence spaces derived by the triple band generalized Fibonacci difference operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
S. A. Mohiuddine ◽  
M. Mursaleen ◽  
Khursheed J. Ansari
Keyword(s):  
Hausdorff Measure ◽  
Difference Operator ◽  
Matrix Operator ◽  
Sufficient Condition ◽  
Topological Properties ◽  
Necessary And Sufficient Condition ◽  
Band Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings ◽  
Triple Band

AbstractIn this article we introduce the generalized Fibonacci difference operator $\mathsf{F}(\mathsf{B})$ F ( B ) by the composition of a Fibonacci band matrix and a triple band matrix $\mathsf{B}(x,y,z)$ B ( x , y , z ) and study the spaces $\ell _{k}( \mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) . We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces $\ell _{k}(\mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) to space $\mathsf{Y}\in \{\ell _{\infty },c_{0},c,\ell _{1},cs_{0},cs,bs\}$ Y ∈ { ℓ ∞ , c 0 , c , ℓ 1 , c s 0 , c s , b s } and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces $\ell _{k}(\mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) to $\mathsf{Y}\in \{ \ell _{\infty }, c, c_{0}, \ell _{1},cs_{0},cs,bs\} $ Y ∈ { ℓ ∞ , c , c 0 , ℓ 1 , c s 0 , c s , b s } using the Hausdorff measure of non-compactness.

scholarly journals On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 789
Author(s):  
Orhan Tuğ ◽  
Vladimir Rakočević ◽  
Eberhard Malkowsky
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Double Sequences ◽  
Real Numbers ◽  
Band Matrix ◽  
Double Sequence Spaces ◽  
Double Sequence Space ◽  
Inclusion Relations ◽  
Matrix Mappings

Let E represent any of the spaces M u , C ϑ ( ϑ = { b , b p , r } ) , and L q ( 0 < q < ∞ ) of bounded, ϑ -convergent, and q-absolutely summable double sequences, respectively, and E ˜ be the domain of the four-dimensional (4D) infinite sequential band matrix B ( r ˜ , s ˜ , t ˜ , u ˜ ) in the double sequence space E, where r ˜ = ( r m ) m = 0 ∞ , s ˜ = ( s m ) m = 0 ∞ , t ˜ = ( t n ) n = 0 ∞ , and u ˜ = ( u n ) n = 0 ∞ are given sequences of real numbers in the set c ∖ c 0 . In this paper, we investigate the double sequence spaces E ˜ . First, we determine some topological properties and prove several inclusion relations under some strict conditions. Then, we examine α -, β ( ϑ ) -, and γ -duals of E ˜ . Finally, we characterize some new classes of 4D matrix mappings related to our new double sequence spaces and conclude the paper with some significant consequences.

scholarly journals On Generalized p , q -Euler Matrix and Associated Sequence Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Mohammad Mursaleen
Keyword(s):  
Sequence Spaces ◽  
Topological Properties ◽  
Geometric Properties ◽  
Inclusion Relations ◽  
Matrix Mappings ◽  
Euler Matrix

In this study, we introduce new BK -spaces b s r , t p , q and b ∞ r , t p , q derived by the domain of p , q -analogue B r , t p , q of the binomial matrix in the spaces ℓ s and ℓ ∞ , respectively. We study certain topological properties and inclusion relations of these spaces. We obtain a basis for the space b s r , t p , q and obtain Köthe-Toeplitz duals of the spaces b s r , t p , q and b ∞ r , t p , q . We characterize certain classes of matrix mappings from the spaces b s r , t p , q and b ∞ r , t p , q to space μ ∈ ℓ ∞ , c , c 0 , ℓ 1 , b s , c s , c s 0 . Finally, we investigate certain geometric properties of the space b s r , t p , q .

scholarly journals A new perspective on paranormed Riesz sequence space of non-absolute type

2015 ◽  
Vol 3 (4) ◽  
pp. 150 ◽  
Author(s):  
Murat Candan
Keyword(s):  
Sequence Space ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Band Matrix ◽  
Current Article ◽  
Matrix Class ◽  
Alpha Beta ◽  
New Perspective ◽  
Convergent Sequences

<p>The current article mainly dwells on introducing Riesz sequence space \(r^{q}(\widetilde{B}_{u}^{p})\) which generalized the prior studies of Candan and Güneş [28], Candan and Kılınç [30]  and consists of all sequences whose \(R_{u}^{q}\widetilde{B}\)-transforms are in the space \(\ell(p)\), where \(\widetilde{B}=B(r_{n},s_{n})\) stands for double sequential band matrix \((r_{n})^{\infty}_{n=0}\) and \((s_{n})^{\infty}_{n=0}\) are given convergent sequences of positive real numbers. Some topological properties of the new brand sequence space have been investigated as well as \(\alpha\)- \(\beta\)-and \(\gamma\)-duals. Additionally, we have also constructed the basis of \(r^{q}(\widetilde{B}_{u}^{p})\). Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.</p>

scholarly journals The application domain of difference type matrix D(r,0,s,0,t) on some sequence spaces

2020 ◽  
pp. 32-32
Author(s):  
Avinoy Paul ◽  
Binod Tripathy
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Application Domain ◽  
Topological Properties ◽  
Difference Type ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper we introduce new sequence spaces with the help of domain of matrix D(r,0,s,0,t), and study some of their topological properties. Further, we determine ? and ? duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings.

scholarly journals On some new paranormed sequence spaces defined by the matrix (D )(r,0,0,s)

2021 ◽  
Vol 40 (3) ◽  
pp. 779-796
Author(s):  
Avinoy Paul
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.

Electron Microscopy of Nucleic Acids

1974 ◽  
Vol 32 ◽  
pp. 302-303
Author(s):  
Norman Davidson
Keyword(s):  
Electron Microscopy ◽  
Nucleic Acids ◽  
Basic Protein ◽  
Molecular Biologist ◽  
Topological Properties ◽  
Protein Film ◽  
Polynucleotide Chain

The basic protein film technique for mounting nucleic acids for electron microscopy has proven to be a general and powerful tool for the working molecular biologist in characterizing different nucleic acids. It i s possible to measure molecular lengths of duplex and single-stranded DNAs and RNAs. In particular, it is thus possible to as certain whether or not the nucleic acids extracted from a particular source are or are not homogeneous in length. The topological properties of the polynucleotide chain (linear or circular, relaxed or supercoiled circles, interlocked circles, etc. ) can also be as certained.

The Effect of Topological Properties on Duration Perception of Oddball Stimuli

2013 ◽  
Vol 45 (12) ◽  
pp. 1324-1333
Author(s):  
Baolin LI ◽  
Youguo CHEN ◽  
Xiangyong YUAN ◽  
Jackson Todd ◽  
Xiting HUANG
Keyword(s):  
Topological Properties
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