Introduction: At high magnetic field strength, B1 inhomogeneity causes undesired effects of non-uniformity in SNR and contrast. For slice selective excitation, 3D RF pulse design proposed in [1,2,3], can be used to mitigate this B1 inhomogeneity effect. These designs are based on playing kz sinc “spokes” of different amplitude at a number of (kx,ky) locations around the k-space origin. The sinc...

Given an order-enriched category, it is known that all its KZ-monadic subcategories can be described by Kan-injectivity with respect to a collection of morphisms. We prove the analogous result for Kan-injectivity with respect to a collection H of commutative squares. A square is called a Kan-injective consequence of H if by adding it to H Kan-injectivity is not changed. We present a sound logic...

We study approximation of Boolean functions by low-degree polynomials over the ring Z/2kZ. More precisely, given a Boolean function F : {0,1}n {0,1}, define its k-lift to be F : {0,1}n {0,2k-1} by Fk(x) = 2k-F(x) mod 2k$. We consider the fractional agreement (which we refer to as d,k(F)) of Fk(x) with degree d polynomials from Z/2kZ[x1,...,xn]. Our results are the following: 1. Increasing k can...

We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are generated by elements of the symmetric group S n. We separately investigate the case S 4. In this case we solve the corresponding KZ-equation in the explicit form.

We establish an equivalence between two approaches to quantization of irreducible symmetric spaces compact type within the framework quasi-coactions, one based on Enriquez-Etingof cyclotomic Knizhnik-Zamolodchikov (KZ) equations and other Letzter-Kolb coideals. This can be upgraded that ribbon braided then associated reflection operators (K-matrices) become a tangible invariant quantization. As...

The coronavirus disease (COVID-19) pandemic has been the largest public health emergency in recent decades. While there have many epidemiology studies on this pandemic, less research done to examine its indirect impact mortality. This paper utilizes Kolmogorov-Zurbenko (KZ) filter chronic kidney (CKD) mortality trend Florida hospitals and finds an of namely excess CKD deaths due pandemic-period...

We use the double affine Hecke algebra of type GLN to construct an explicit consistent system of q-difference equations, which we call the bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik’s quantum affine KZ equations associated to principal series representations of the underlying affine Hecke algebra, a compatible system of q-difference equations ac...