We onsider ”Riesz Theorem” in the 2-inner product spaces and give some results in this field. Also, we give some characterizations about 2-inner product spaces in b-approximation theory. AMS Mathematics Subject Classification (2000): 41A65, 41A15

has been introduced by several authors like Ahmed and Hamouly [1], Kohli and Kumar [5], Biswas [4], etc. Also the notion of fuzzy norm on a linear space was introduced by Katsaras [9]. Later on many other mathematicians like Felbin [3], Cheng and Mordeso [10], Bag and Samanta [6], etc, have given different definitions of fuzzy normed spaces. In recent past lots of work have been done in the top...

The notion of inner-product encryption (IPE), introduced by Katz, Sahai, and Waters at Eurocrypt 2008, is a generalization of identity-based encryption in which ciphertexts and secret keys are associated to vectors in some finite field. In an IPE scheme, a ciphertext can only be decrypted by a secret key if the vector associated with the latter is orthogonal to that of the ciphertext. In its hi...

Bayesian networks have become one of the major models used for statistical inference. We study the question whether the decisions computed by a Bayesian network can be represented within a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. As main results we establish upper and lower bounds on the dimension of the inner product space for Bay...

1 Background We begin by recalling the solution of the vibrating string problem and Sturm-Liouville problems. When we solve the problem of the vibrating string using the technique of separation of variables, the differential equation involving the space variable x, and assuming constant mass density, is y (x) + ω 2 c 2 y(x) = 0, (1.1) which we can write as an eigenvalue problem y (x) + λy(x) = ...

In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages. Given a secret key for a function f and a ciphertext for a message x, a decryptor learns f(x) and nothing else about x. Inner product encryption is a special case of functional encryption where both secret keys and ciphertexts are associated with vectors. The combination of...

This paper addresses the nearest neighbor search problem under inner product similarity and introduces a compact code-based approach. The idea is to approximate a vector using the composition of several elements selected from a source dictionary and to represent this vector by a short code composed of the indices of the selected elements. The inner product between a query vector and a database ...

Deniable encryption (Canetti et al. CRYPTO ’97) is an intriguing primitive that provides a security guarantee against not only eavesdropping attacks as required by semantic security, but also stronger coercion attacks performed after the fact. The concept of deniability has later demonstrated useful and powerful in many other contexts, such as leakage resilience, adaptive security of protocols,...

Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits aredescribed via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that preserve them. Suchstates are obtained by stabilizer circuits (consisting of CNOT, Hadamard and Phase only) and can be represented compactly onconventio...