Hom-Akivis algebras

Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra (i.e. a Hom-nonassociative algebra) is a Hom-Akivis algebra. It is shown that non-Hom-associative algebras can be obtained from nonassociative algebras by twisting along algebra automorphisms while Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms. It is pointed out that a Hom-Akivis algebra associated to a Hom-alternative algebra is a Hom-Malcev algebra.Comment: 15 pages, 0 figure, a section and references are adde

Classifying Two-dimensional Hyporeductive Triple Algebras

Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple systems) and two-dimensional real Bol algebras is given.Comment: 12 pages; 0 figur

Effects of some environmental factors on the fecundity of Tilapia species (Family Cichlidae) in Kigera Reservoir, New Bussa

The effects of some environmental factors on the fecundity of Tilapia species (Family Cichilidae) was carried out at the Kigera dam. Four Tilapia species caught were Tilapia zilli, Hemichromis fasciatus, Sarotherodon galilaeus and Oreochromis niloticus while the environmental factors considered were water temperature, Dissolved Oxygen, pH value, level of rainfall and rate of sunshine and range of time. 43 fish comprising of 25 male with (58.1%) and 18 females having (41.9%) were studied with 74.42% been sexually matured. Both high levels of rainfall and dissolved oxygen favoured fecundity. The spawning peak occurred in (July), environmental factors monitored indicated that dissolved oxygen ranges from 3.7 to 4.45mg/lit rainfall ranges from (34.90mm to 237.80mm) sunshine ranges from (5hrs-8hrs) and pH ranges from (7.35-7.45). The spawning of these species in their natural or hatchery condition is therefore best achieved during the peak of raining seaso

Evans function and Fredholm determinants

We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example reaction-diffusion or solitary wave equations. The Evans function and transmission coefficient, which are both finite determinants, are natural tools for both analytic and numerical determination of eigenvalues of such linear operators. However, inverting the eigenvalue problem by the free state operator generates a natural linear integral eigenvalue problem whose solvability is determined through the corresponding infinite Fredholm determinant. The relationship between all three determinants has received a lot of recent attention. We focus on the case when the underlying Fredholm operator is a trace class perturbation of the identity. Our new results include: (i) clarification of the sense in which the Evans function and transmission coefficient are equivalent; and (ii) proof of the equivalence of the transmission coefficient and Fredholm determinant, in particular in the case of distinct far fields.Comment: 26 page

Two-Hop Interference Channels: Impact of Linear Time-Varying Schemes

We consider the two-hop interference channel (IC) with constant real channel coefficients, which consists of two source-destination pairs, separated by two relays. We analyze the achievable degrees of freedom (DoF) of such network when relays are restricted to perform scalar amplify-forward (AF) operations, with possibly time-varying coefficients. We show that, somewhat surprisingly, by providing the flexibility of choosing time-varying AF coefficients at the relays, it is possible to achieve 4/3 sum-DoF. We also develop a novel outer bound that matches our achievability, hence characterizing the sum-DoF of two-hop interference channels with time-varying AF relaying strategies.Comment: To appear in Proc. of ISIT 2013 (proof of lemma added

Understanding Early Withdrawals From Retirement Accounts

Examines early withdrawals from IRAs and 401(k)s by demographics, education, income, and reason, including job loss, poor health, and college costs. Suggests policies to expand plan participation, preserve retirement savings, and increase other savings