introduction: complete knowledge of root canal curvature is a critical factor in successful dental treatment .the aim of this study was to investigate the direction, radius and degree of curvature of maxillary anterior teeth and the relation between radius and degree of curvature in babol city. methods &materials;: this study was performed on 242 anterior teeth radiographs were taken by periapi...

We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point arithmetic. The modular polynomials are converted into integers using Kronecker substitution (evaluation at a sufficiently large integer). With some control ...

We present a source-to-source compiler that processes matrix formulae in the form of Kronecker product factorizations. The Kronecker product notation allows for simple expressions of algorithms such as Walsh-Hadamard, Haar, Slant, Hartley, and FFTs as well as transpositions and wavelet transforms. The compiler is based on a set of term rewriting rules that translate high level matrix descriptio...

We study the Kronecker symbol ( s t ) for the sequence of the convergents s/t of a purely periodic continued fraction expansion. Whereas the corresponding sequence of Jacobi symbols is always periodic, it turns out that the sequence of Kronecker symbols may be aperiodic. Our main result describes the period length in the periodic case in terms of the period length of the sequence of Jacobi symb...

We give a simple combinatorial proof of Ram’s rule for computing the characters of the Hecke Algebra. We also establish a relationship between the characters of the Hecke algebra and the Kronecker product of two irreducible representations of the Symmetric Group which allows us to give new combinatorial interpretations to the Kronecker product of two Schur functions evaluated at a Schur functio...

The paper presents a system theoretic analysis of network-of-networks which are formed from smaller factor networks via graph Kronecker products. We provide a compositional framework for extending trajectories, stabilizability, controllability and observability of the factor networks to that of the composite network-of-networks. We proceed to delve into the effectiveness of applying these compo...

We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of Sn, which we apply to obtain various explicit estimates. Notably, we extend Sylvester’s unimodality of q-binomial coefficients ( n k ) q as polynomials in q to derive sharp bounds on the differences of their consecutive coefficients. We then derive effective asymptotic lower bo...

| The paper gives a positive answer to an open problem-whether there exists some family of canonical forms that would include both the Generalized Reed-Muller Forms and the Kronecker Forms as its special cases. We call the new forms Generalized Kronecker Forms. We present also the corresponding decision diagrams. They can be used for representation of large functions and also for optimal synthe...

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

This paper deals with design of continuous-time robustly stabilizing Proportional-Integral (PI) controllers for interval systems using the combination of Kronecker summation method, sixteen plant theorem and an algebraic approach to controller tuning. The effectiveness and practical applicability of the proposed method is demonstrated in both simulation and real experiments including control of...