The Tamari lattice Tn was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Although in several related lattices, the number of maximal chains is known, quoting Knuth, “The enumeration of such paths in Tamari lattices remains mysterious.” The lengths of maximal chains vary over a great range. In this paper, we focu...

Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction D, and Forney’s code formula are classical constructions that produce such lattices explicitly from a family of nested binary linear codes. In this paper, we investigate these three closely related constructi...

In this paper, we consider representations of p p -adic classical groups parabolically induced from the products shifted Speh and unitary Arth...

This paper is devoted to proposing an approximate numerical algorithm based on the use of state parameterization technique in order find solution optimal control problem (OCP). An explicit formula for new shifted wavelet (NSW) functions constructed. A that expresses first-order derivative NSW terms their original established. The development our suggested algorithms begins with extraction a ope...

Taking t at random, uniformly from [0,T], we consider the kth moment, with respect to t, of random variable corresponding 2?th moment ?(1/2+ix) over interval x?(t,t+1], where ?(s) is Riemann zeta function. We call these ‘moments moments’ function, and present a conjecture for their asymptotics, when T??, integer k,?. This motivated by comparisons results moments characteristic polynomials unita...

The amplitude of the photoacoustic effect for an optical source moving at the sound speed in a one-dimensional geometry increases linearly in time without bound in the linear acoustic regime. Here, use of this principle is described for trace detection of gases, using two frequency-shifted beams from a CO2 laser directed at an angle to each other to give optical fringes that move at the sound s...

We give explicit evaluations of the linear and non-linear Euler sums hyperharmonic numbers $$h_{n}^{\left( r\right) }$$ with reciprocal binomial coefficients. These enable us to extend closed form formula an arbitrary integer r. Moreover, we reach at formulas for shifted Euler-type harmonic numbers. All are provided in terms Riemann zeta values, sums.