In this paper employing Routh's table, a geometrical stability criterion for the analysis of linear time-invariant system is formulated. The proposed stability criterion is applied for the system, whose characteristic equation having complex coefficients. For this Routh like table is presented with complex terms and the signs pair-wise elements with the first column of the table are observ...

Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of Yang-Mills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and covariant anomalies are determined. A geometrical realization of the BRS/anti-BRS algebra is prese...

We introduce a computable estimator of block entanglement entropy for many-body spin systems admitting total singlet ground states. Building on a simple geometrical interpretation of entanglement entropy of the so-called valence bond states, this estimator is defined as the average number of common singlets to two subsystems of spins. We show that our estimator possesses the characteristic scal...

Though manifold learning has been successfully applied in wide areas, such as data visualization, dimension reduction and speech recognition; few researches have been done with the combination of the information theory and the geometrical learning. In this paper, we carry out a bold exploration in this field, raise a new approach on face recognition, the intrinsic α-Rényi entropy of the face im...

In this study, characterization of monochlorophenols (o-, m-, p-chlorophenol) has been observed by using FTIR spectroscopy as well as the effects of molecule symmetry on vibrational frequencies of molecule. Vibrational modes of monochlorophenols investigated by means of ATR which is the best choice for liquid phase. The observed infrared bands of monochlorophenols are assigned with their geomet...

The singularities that we consider are the characteristic non-smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges. We describe here a method to compute their singularity exponents and the associated angular singular functions. We present the implementation of this method in a program whose input data are g...

Application of stochastic geometry methods to pattern recognition is analyzed. The paper is based on Trace-transformations of original images introduced in [1] into images on the Mobius band. Trace–transformation is a new geometrical transformation, which is connected with image scanning on complex trajectories, including random parameters trajectories. Based on this new geometric transformatio...

Let m be a random tessellation in R, d ≥ 1, observed in the window Wρ = ρ1/d[0, 1], ρ > 0, and let f be a geometrical characteristic. We investigate the asymptotic behaviour of the maximum of f(C) over all cells C ∈ m with nucleus in Wρ as ρ goes to infinity. When the normalized maximum converges, we show that its asymptotic distribution depends on the so-called extremal index. Two examples of ...

A new Einstein–Hilbert type action of superon-graviton model (SGM) for space-time and matter is obtained based upon the geometrical arguments of the higher symmetric (SGM) space-time. SGM action is invariant under [global NL SUSY] ⊗ [local GL(4,R)] ⊗ [local Lorentz]⊗ [global SO(N)]. The explicit form of SGM action is given in terms of the fields of the graviton and superons by using the affine ...

Geometries of ethylene clusters (C 2 H 4) n in the range of n ≤ 25 are optimized with the intermolecular potential based on the ab initio calculations of the dimer. The heuristic method combined with geometrical perturbations is used for geometry optimization. Ethylene clusters do not take the icosahedral motif characteristic of some van der Waals molecular clusters. The structural evolution of...