We give a construction of quantum LDPC codes dimension $\Theta(\log N)$ and distance $\Theta(N/\log as the code length $N\to\infty$. Using product chain complexes this also provides family $\Omega(N^{1-\alpha/2}/\log $\Omega(N^\alpha \log N)$, where $0 \le \alpha < 1$. introduce study new operation called lifted product, which naturally generalizes operations for complexes. Moreover, simple byp...

A new type of polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

In this paper, we study the approximate biprojectivity and biflatness of a Banach algebra A find some relations between theses concepts with ?-amenability ? -contractibility, where is character on A. Among other things, show that ?-Lau product L1(G) ?? A(G) approximately biprojective if only G finite, are group Fourier locally compact G, respectively. We also characterize biflat semigroup algeb...

A new polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.

There are two de Rham complexes in diffeology. The original one is due to Souriau and the other singular complex defined by a simplicial differential graded algebra. We compare first cohomology groups of within Čech–de spectral sequence making use factor map which connects complexes. As consequence, it follows that algebra irrational torus $T_\theta$ isomorphic tensor product exterior genera...

Malaria causes high global mortality and morbidity annually. Plasmodium knowlesi has been recognised as the fifth human Plasmodium sp. and its infection is widely distributed in Southeast Asia. Merozoite surface protein-119 (MSP-119) appears as a potential candidate for malaria blood stage vaccine as it could induce protective immunity. In this study, codon optimized P. knowlesi MSP-119 (pkMSP-...

A study was conducted to extend the sequential probability ratio testing (SPRT) procedure with the polytomous model under some practical constraints in computerized classification testing (CCT), such as methods to control item exposure rate, and to study the effects of other variables, including item information algorithms, test difficulties, item pool sizes, and widths of the indifference regi...