Stochastic differential equations have been intensively used to analyze data from physics, finance, engineering, medicine, biology, and forestry. This study proposes a general stochastic dynamical model of a forest stand development which includes random forces governing the dynamic of multivariate distribution of tree size variables. The dynamic of the multivariate probability density function of tree size components (diameter, height, crown base height, crown width and so on) in a stand is described by a mixed effect parameters Gompertz-type multivariate stochastic differential equation (SDE). The advantages of SDE method are that it do not need to choose many different equations to be tried, it relates the tree size components dynamic against the age dimension (time), and consider the underlying covariance structure driving changes in the tree (stand) size variables. SDE model allows us a better understanding of biological processes driving the dynamics of natural phenomena. The new derived multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate distributions can be applied for the modeling of stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, their increments and much more. This study introduces general multivariate mutual information measures based on the differential entropy to capture multivariate interactions between state variables. The purpose of the present study is therefore to experimentally confirm the effectiveness of using multivariate mutual information measures to reconstruct multivariate interactions in state variables.

The dihedral group represents a group of symmetries of a regular polygon. Moreover, it is generated by rotation and axial symmetries. Due to this structure, in a recently published paper, we analyzed the HX-groups associated with them and we computed the commutativity degree of the associated HX-groups. Since there is an interesting connection between the HX-groups and the complete hypergroups- both of them can be constructed using the structure of a group, in this paper, we aim to determine the relationships between the lattice of the dihedral group and the lattice of the associated HX-groups, as well as that of the associated complete hypergroups. Furthermore, we will present some conditions to describe the modular and the distributive lattices, using elements from hypercompositional algebra. This has the advantage that the interaction called hyperproduct or hyperoperation between two elements of the considered set is not anymore just an element, as in the classical algebra, but a subset of the support set.

A new generalization of the log-logistic distribution with increasing, decreasing, unimodal and bathtub hazard rates was proposed and studied, extending the log-logistic distribution by adding an extra shape (or skewness) parameter to the existing distribution, leading to greater flexibility in analysing and modeling various data types. Some of its mathematical and statistical properties were derived and model parameters estimated using the classical method especially the maximum likelihood approach and the Bayesian approach. The new hazard rate can be “increasing”, “decreasing”, “unimodal”, and “bathtub” shapes. The flexibility and usefulness of the proposed distribution was applied to three different real-life data sets with symmetric and asymmetric shapes and as well as different failure rate shapes and compared to other competitive parametric survival models. Finally, the proposed distribution is applied to regression survival analysis and verified that it is closed under both proportional hazard and accelerated failure time models that is a great contribution to the field of survival and reliability analysis and other disciplines in the areas of economics and demographic studies.

A symmetry assisted approach to multidimensional vibronic problem: theoretical background and some chemical applications

Boris Tsukerblat¹, Andrew Palii²

¹Ben-Gurion University of the Negev, Department of Chemistry, Beer-Sheva, Israel

² Institute of Problems of Chemical Physics (IPCP), Chernogolovka, Moscow Region, Russia

The classical treatment of the nuclear motion is invalid (despite the difference in masses of electrons and nuclei) in the region of crossover of the terms or, more commonly, when we are dealing with the orbitally degenerate or pseudo degenerate levels. To overcome significant limitations implied by the adiabatic approximation, we propose a symmetry-adapted approach aimed to the accurate solution of the quantum-mechanical (dynamic) vibronic problem in large scale molecular systems. The algorithm for the solution of the eigen-problem with a huge Hilbert space takes full advantage of the point symmetry arguments. Applying the successive coupling of the bosonic creation operators, we introduce complex irreducible tensors that can be referred to as multivibronic operators. The generated vibrational basis is coupled to the electronic one to get the symmetry adapted electron-vibrational basis within which the full matrix of the Hamiltonian is blocked to maximum extent according to the irreducible representations of the point group. The approach allows to treat optical and thermodynamic properties of the nanoscale multilevel vibronic system, such as mixed-valence molecules and impurity centers in crystals. The developed technique is applied to consideration of 2e-reduced mixed-valence dodecanuclear Keggin anion in which the electronic pair is delocalized over twelve sites, tetrameric systems in which two mobile electrons are employed to encode binary information in molecular quantum cellular automata, complex organic systems exhibiting unusual intervalence optical vibronically assisted absorption.

Acknowledgements: Support from Russian Science Foundation (No. 20-13-00374) and the Ministry of Science and Higher Education (creation of the Lab. of Molecular Magnetic Nanomaterials at IPCP, No. 14.W03.31.0001) is acknowledged.

The running path of automated guided vehicles（AGVs）in the automated terminal is affected by the storage location of containers, and the running time caused by congestion, deadlock and other problems during the driving process is uncertain. In this paper, considering the different AGVs congestion conditions along the path, a symmetric triangular fuzzy number is used to describe the AGVs operation time distribution, and a multi-objective scheduling optimization model is established to minimize the risk of quay cranes (QCs) delay and the shortest AGVs operation time. An improved genetic algorithm was designed to verify the effectiveness of the model and algorithm by comparing the results of the AGVs scheduling and container storage optimization model based on fixed congestion coefficient under different example sizes. The results show that considering the AGVs task allocation and container storage location allocation optimization scheme with uncertain running time can reduce the delay risk of QCs, reduce the maximum completion time, and have important significance for improving the loading and unloading efficiency of the automated terminal.