List homomorphisms generalize list colourings in the following way: Given graphs G; H , and lists L(v) V (H); v 2 V (G), a list homomorphism of G to H with respect to the lists L is a mapping f : V (G) ! V (H) such that uv 2 E (G) implies f (u)f(v) 2 E (H), and f (v) 2 L(v) for all v 2 V (G). The list homomorphism problem for a xed graph H asks whether or not an input graph G together with list...

Fischer, Lynch, and Paterson showed in a fundamental paper that achieving a distributed agreement is impossible in the presence of one faulty processor. This result was later extended by Moran and Wolfstahl who showed that it holds for any task with a connected input graph and a disconnected decision graph. In this paper we extend that latter result, and in fact we set an exact borderline betwe...

We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a given word. Our main result is that the length of the element represented by a word in a free solvable group can be determined in polynomial time. Let P = 〈X | R〉 be a group presentation. Let F be free on X, let ...

We define an obstruction for a knot to be ?[?]-homology ribbon, and use this provide restrictions on the integers that can occur as triple linking numbers of derivative links knots are either homotopy ribbon or doubly slice. Our main application finds new non-doubly slice knots. In particular, gives information solvable filtration Taehee Kim: algebraically need not (1)-solvable, (0.5, 1)-solvab...

in this paper, we verify the solvability of free product of finite cyclic groups with topological methods. we use cayley graphs and everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. in particular, using these methods, we prove that the commutator subgroup of $mathbb{z}_{m}*mathbb{z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

in this paper‎, ‎we give a complete proof of theorem 4.1(ii) and a new‎ ‎elementary proof of theorem 4.1(i) in [li and shen‎, ‎on the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ j‎. ‎algebra, ‎323  (2010) 1349--1357]‎. ‎in addition‎, ‎we also give a generalization of baer's theorem‎.

Let A be a finite dimensional associative algebra with derivations over field of characteristic zero, i.e., an whose structure is enriched by the action Lie L derivations, and let cnL(A), n≥1, its differential codimension sequence. Such sequence exponentially bounded expL⁡(A)=limn→∞⁡cnL(A)n integer that can computed, called PI-exponent A. In this paper we prove for any L, expL⁡(A) coincides exp...

A novel analytically solvable deformed Woods−Saxon potential is investigated by means of the Supersymmetric Quantum Mechanics. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. The energy levels are obtained for any l-state. The interrelations for some nuclear scattering processes are also discussed. PACS No. 03.65.Ca, 03.65.Ge, 03.65.Nk