Mathematical Modeling of Tidal Effects in Groundwater

This paper presents a special use of the linear poroelasticity theory to describe tidally induced groundwater oscillations. Two models of oscillation inducing mechanism make use of this theory to predict groundwater level fluctuations. The numerical solutions of both models are presented and compared with well water level measurement obtained in Police Basin, north-east Bohemia.     

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

A Lie symmetry approach for the solution of the inverse kinematics problem

In this paper, it is considered the inverse kinematics problem, which is faced from a differential point of view. In particular, it is shown that an asymptotic inverse kinematics can be interpreted as a Lie symmetry of the direct kinematics. A parameterization of all Lie symmetries of the direct kinematics is proposed, and the classical Newton and gradient method are obtained as particular cases.     

Diffusion of biostimulators into plant tissues

Biostimulators are substances able to enhance the immune system of cultivated crops and support plant metabolism. Their utilization helps to reduce the amount of chemicals used in agriculture. To perform the desired effect, a biostimulator must be able to penetrate into the plant tissue. The time of penetration however, is limited, since the biostimulator must remain in a liquid state. This is of great importance—especially in field conditions, where the treated plants are exposed to different weather condition and other extrinsic factors. A mathematical model based on diffusion mechanisms has been elaborated to describe the biostimulator transport process from penetration of the leaves into the plant’s inner tissues. By means of the effective diffusion coefficient of the prepared specific protein hydrolyzate, this model can be used to estimate the time necessary for the uptake of the minimal active amount of the biostimulator.     

The dual of a constacyclic code,self dual,reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3

Over finite local Frobenius non-chain rings with nilpotency index 3 and when the length of the codes is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of $\gamma$-constacyclic codes is established and the algebraic characterization of self-dual $\gamma$-constacyclic codes, reversible $\gamma$-constacyclic codes and $\gamma$-constacyclic codes with complementary dual are given. Generators for the dual code are obtained from those of the original constacyclic code.     

Homomorphisms of matrix algebras and constructions of Butson–Hadamard matrices

An $n\times n$ matrix $H$ is Butson–Hadamard if its entries are $k$th roots of unity and it satisfies $H{H}^1=n{I}_n$. Write $\mathrm{BH}(n,k)$ for the set of such matrices.Suppose that $k=p^{\alpha }{q}^{\beta }$ where $p$ and $q$ are primes and $\alpha \ge 1$. A recent result of Östergård and Paavola uses a matrix $H\in \mathrm{BH}(n,pk)$ to construct $H^{\prime }\in \mathrm{BH}(pn,k)$. We simplify the proof of this result and remove the restriction on the number of prime divisors of $k$. More precisely, we prove that if $k=mt$, and each prime divisor of $k$ divides $t$, then we can construct a matrix $H^{\prime }\in \mathrm{BH}(mn,t)$ from any $H\in \mathrm{BH}(n,k)$.     

Synthesis of 1-aryl-3H-[1,2,5]triazepino[5,4-a]benzimidazol-4(5H)-ones and quantum chemical investigation of the rotamers of the Boc-protected hydrazide key intermediate

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