We present a linear realizability technique for building Partial Equivalence Relations (PER) categories over Linear Combinatory Algebras. These PER categories turn out to be linear categories and to form an adjoint model with their co-Kleisli categories. We show that a special linear combinatory algebra of partial involutions, arising from Geometry of Interaction constructions, gives rise to a ...

It has been unknown since the time of Euler whether or not time-periodic sound wave propagation is physically possible in the compressible Euler equations, due mainly to the ubiquitous formation of shock waves. The existence of such waves would confirm the possibility of dissipation free long distance signaling. Following our work in [27], we derive exact linearized solutions that exhibit the s...

Partial words, which are sequences that may have some undefined positions called holes, can be viewed as sequences over an extended alphabet A = A ∪ { }, where stands for a hole and matches (or is compatible with) every letter in A. The subword complexity of a partial word w, denoted by pw(n), is the number of distinct full words (those without holes) over the alphabet that are compatible with ...

The study included a sample of 333 preschool children (162 male and 171 female) at the time of school enrolment. Study subjects were recruited from the population of children in kindergartens in the cities of Novi Sad, Sombor, Sremska Mitrovica and Backa Palanka (Province of Voivodina, Serbia). Eight anthropometric variables, seven motor variables and one cognitive variable were analyzed to ide...

Let θ = [0; a1, a2, . . .] be an algebraic number of degree at least three. Recently, we have established that the sequence of partial quotients (a`)`≥1 of θ is not too simple and cannot be generated by a finite automaton. In this expository paper, we point out the main ingredients of the proof and we briefly survey earlier works.

Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$‎ ‎x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x)‎,$$ ‎we find the coefficients $b_{i,j}^{(p,q,ell‎ ,‎,r)}$ in the expansion‎ $$‎ ‎x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell‎ ‎}y^{r}f^{(p,q)}(x,y) =sumli...

Mitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS) syndrome is a rare congenital disorder of mitochondrial DNA, presenting a wide range of clinical symptoms comprising headaches, seizures, aphasia, hearing loss, visual defects, and hemiparesis. Herein we report a case of a previously asymptomatic 40-year-old male who presented with recurrent headache, seiz...

This paper investigates the use o f partial functions in genetic programming. Previous work has shown that the convergent behaviour of populations of partial functions is very similar to that of populations of total functions. However the convergence rates o f populations of partial functions have been slower. The results presented here demonstrate a significant improvement in the rate o f conv...

Two peroxidases (EC. 1.11.1.7), POD I and POD II were purified from the roots of cultivatedRaphanus sativus L. Var. Cicil by one step ion-exchange chromatography after fractionation by acetone. The molecular weight of these enzymes were 43000 and 41000 Daltons and RZ 1.2 and 2.0 for POD I and POD II, respectively. Both enzymes consisted of a single polypeptide chain on SDS-PAGE. The maximum...

A partial algebra A = (A, F ) is called surjective if each of its elements lies in the range of some of its operations. By a transfinite iteration construction over the class of all ordinals it is proved that in each partial algebra A there exists the largest surjective subalgebra Skr A, called the surjective kernel of A. However, what might be found a bit surprising, for each ordinal α there i...