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With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that ̂ B p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), ̂ F s,q p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), if 0 < p < 1, 0 < q < 1, s ∈ R, while ̂ B p (Rn) = B s−n ( 1 p −1 ) ,q 1 (R ), ̂ F s,q p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), if 0 < p < 1, 1 ≤ q < +∞, s ∈ R, and ̂ B p (Rn) = B p (R), ̂ F s,q p (Rn) = F s,1 p (R), if 1 ≤ p < +∞, 0 < q < 1...
A fully working reduced Enigma has been used very successfully in numerous public lectures, in school talks, and in university seminars. Hands-on demonstrations of the reduced Enigma dramatically brings alive ideas about design, codes, permutations and groups. As a working trapdoor function, the reduced Enigma also provides an unusually clear introduction to public key cryptography. This articl...
............................................................................................................................................................................... 623 Introduction .......................................................................................................................................................................... 624 Case Study Sites ...............
INTRODUCTION .............................................................. 609 MATERIALS AND METHODS ...................... ........................... 609 Media..................................................................... 609 Strains .................................................................... 609 S. typhimurium ............................................................. 609...
1, R.Senthil kumar, 2, R.M.Sekar, 3, L.Hubert Tony Raj, 4, I.Gerald Christopher Raj PG scholar, Department of EEE, PSNA College of Engineering & Technology Dindigul – 624 622, Tamilnadu, India. Associate Professor, Department of EEE, PSNA College of Engineering & Technology Dindigul – 624 622, Tamilnadu, India. PG scholar, Department of EEE, PSNA College of Engineering & Technology Dindigul – 6...
Novel species of fungi described in this study include those from various countries as follows: Australia: Banksiophoma australiensis (incl. Banksiophoma gen. nov.) on Banksia coccinea, Davidiellomycesaustraliensis (incl. Davidiellomyces gen. nov.) on Cyperaceae, Didymocyrtis banksiae on Banksia sessilis var. cygnorum, Disculoides calophyllae on Corymbia calophylla, Harknessia banksiae on Banks...
Sufficient conditions are established for the solvability of the boundary value problem dx(t) dt = p(x, x)(t) + q(x)(t), l(x, x) = c(x) , where p : C(I; Rn)× C(I; Rn) → L(I; Rn), q : C(I; Rn) → L(I; Rn), l : C(I, Rn)× C(I; Rn) → Rn, and cn : C(I, Rn) → Rn are continuous operators, and p(x, ·) and l(x, ·) are linear operators for any fixed x ∈ C(I; Rn). 1. Formulation of the Main Results 1.1. Fo...
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