In this paper we combine results from [1] and [3] in order to determine the relationship between the deficiency of a group G and the deficiency of a Rees matrix semigroup S over G; in particular, we investigate how the efficiency of S depends on the efficiency of G. We start by defining semigroup and group presentations. Let A be an alphabet. We denote by A the free semigroup on A consisting of...

That is, W0 is the set of all finite products of the generators, allowing repetitions. Let W signify the larger multiplicative semigroup generated by W0 together with {1/2}. We call W the wild semigroup and W0 the Wooley semigroup. The question we consider is: Which integers belong to these semigroups? The sets of integer elements W(Z) := W ∩ Z and W0(Z) := W0 ∩ Z themselves form multiplicative...

We introduce the notion of ideals in implicative semigroups, and then state the characterizations of the ideals. 2000 Mathematics Subject Classification. 20M12, 06F05, 06A06, 06A12.

Volatility is the key of the option price in the stock market. Changes in volatility will dramatically lead to changes of the option price. One of the most important volatilities is historical volatility (HV ). The HV is essentially the annualized standard deviation of the first order difference of logarithm of the asset price. Therefore, changes in HV in finance may be detected by the variance...

BACKGROUND Klebsiella pneumoniae (KP) expressing hypermucoviscosity phenotype (HV-KP) has abundant capsular polysaccharide (CPS) and is capable of causing invasive syndrome. Sodium salicylate (SAL) reduces the production of CPS. The study was aimed to investigate the relationship between aspirin usage and KP-mediated invasive syndrome and the effect of SAL on HV-KP. METHODS Patients with comm...

BACKGROUND Patients with hallux valgus (HV) frequently present to podiatrists for non-surgical management, with a wide range of concerns including pain, footwear difficulty and quality of life impacts. There is little research evidence guiding podiatrists' clinical decisions surrounding non-surgical management of HV. Thus practitioners rely largely upon clinical experience and expert opinion. T...

In this paper we describe the modulus semigroup of the C0-semigroup associated with the linear differential equation with delay { u1ptq Auptq Lut (t ¥ 0), up0q x∈X, u0 f ∈Lpp h, 0;Xq, in the Banach lattice X Lpp h, 0;Xq, where X is a Banach lattice with order continuous norm. The progress with respect to previous papers is that A may be an unbounded generator of a C0-semigroup possessing a modu...

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. A projective limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this projective limit is isomorphic, as a...

Spinal cord injury (SCI) leads to devastating neurological deficits. Several tissue engineering (TE)-based approaches have been investigated for repairing this condition. Poly (3-hydroxybutyrate-co-3-hydroxyvalerate) (PHB-HV) is found to be particularly attractive for TE applications due to its properties, such as biodegradability, biocompatibility, thermoplasticity and piezoelectricity. Hence,...