In this work, we propose a high resolution Alternating Evolution Discontinuous Galerkin (AEDG) method to solve Hamilton-Jacobi equations. The construction of the AEDG method is based on an alternating evolution system of the Hamilton-Jacobi equation, following the previous work [H. Liu, M. Pollack and H. Saran, SIAM J. Sci. Comput. 35(1), (2013) 122–149] on AE schemes for Hamilton-Jacobi equati...

Let A be a set of 2n points in general position on a plane, and suppose n of the points are coloured red while the remaining are coloured blue. An alternating path P of A is a sequence p1, p2,..., p2n of points of A such that p2i is blue and p2i+1 is red. P is simple if it does not intersect itself. We determine the condition under which there exists a simple alternating path P of A for the cas...

The logic called ATL (Alternating-time Temporal Logic) was introduced, in 1997, as a modal logic of agents. The first direct algorithm to test whether a given ATL-formula θ is satisfiable was provided by V. Goranko and G. van Drimmelen in 2006. Their algorithm is based on alternating infinite tree automata. In 2009, V. Goranko and D. Shkatov proposed a method to test satisfiability of a formula...

A subset S of a poset (partially ordered set) is convex if and only if S contains every poset element which is between any two elements in S. Poset convex subsets arise in applications that involve precedence constraints, such as in project scheduling, production planning, and assembly line balancing. We give a strongly polynomial time algorithm which, given a poset and element weights (of arbi...

During the past years many models of parallel computations have arisen. One of them alternation was introduced in [l] as a generalization of nondeterminism. Several types of alternating machines have been introduced and many results about them have been established. Among the most interesting modifications are the alternating machines with universal states only (here, universally branching Turi...

Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust) correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared with the more tradi...

‎Let $G $ be a finite group and $X$ be a conjugacy class of $G.$ The‎ ‎rank of $X$ in $G,$ denoted by $rank(G{:}X),$ is defined to‎ ‎be the minimal number of elements of $X$ generating $G.$ In this‎ ‎paper we establish the ranks of all the conjugacy classes of‎ ‎elements for simple alternating group $A_{10}$ using the structure‎ ‎constants method and other results established in‎ ‎[A.B.M‎. ‎Bas...

Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...

a r t i c l e i n f o a b s t r a c t In a recently published paper [Z.-J. Xue, S.-Y. Liu, An optimal result on fault-tolerant cycle-embedding in alternating group graphs, Inform. the authors showed that for a set of faulty vertices F in an n-dimensional alternating group graph AG n , AG n − F remains pancyclic if |F | 2n − 6. However, the proof of the result is flawed. We will prove the theore...

The alternating decision tree (ADTree) is a successful classification technique that combines decision trees with the predictive accuracy of boosting into a set of interpretable classification rules. The original formulation of the tree induction algorithm restricted attention to binary classification problems. This paper empirically evaluates several wrapper methods for extending the algorithm...