Given n ∈ Z, its arithmetic derivative n is defined as follows: (i) 0 = 1 = (−1)′ = 0. (ii) If n = up1 · · · pk, where u = ±1 and p1, . . . , pk are primes (some of them possibly equal), then

Let A ⊇ D ⊆ B be two von Neumann algebras together with a common Cartan subalgebra. Then the amalgamated free product M = A ∗D B with respect to the unique conditional expectations from A, B onto D can be considered. In our previous paper [U1], the questions of its factoriality and type classification were discussed in detail, which will be reviewed in §4. The main purpose of the paper is to gi...

The five simple exceptional complex Lie superalgbras of vector fields are described. One of them is new; the other four are explicitely described for the first time. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation. The description of several of the exceptional Lie superalgebras is associated with the Lie superalgebra a...

We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.

background: daylight availability data are essential for designing effectively day lighted buildings. in respect to no available daylight availability data in iran, illuminance data on the south facing vertical surfaces were estimated using a proper method. methods: an illuminance measuring set was designed for measuring vertical illuminances for standard times over 15 days at one hour interval...

In the present work, q-homotopy analysis transform method (q-HATM) was used to generate an analytical solution for moisture content distribution in a one-dimensional vertical groundwater recharge problem. Three scenarios Brooks–Corey model are studied based on linear and nonlinear diffusivity conductivity functions. The governing fractional partial differential equations solved effectively by c...

An inverse design process is applied to determine blade shapes used in vertical axis wind turbines (VAWTs). The method is based on the modified Garabedian-McFadden technique that uses the deviation of the pressure distribution or the velocity distribution on the surface from a target pressure or velocity distribution, and modifies the blade surface in order to reduce this deviation. The method ...

We report 2 cases of Plasmodium falciparum malaria in southern France in a French woman and an American man of Togolese origin who reported no recent travel to malaria-endemic countries. Both infections occurred after a stay near Marseille, which raises the possibility of autochthonous transmission. Entomologic and genotypic investigations are described.

Aquifer test methods have greatly improved in recent years with the advent of inverse analysis, derivative analysis, and diagnostic plots. Updated analyses of past aquifer tests allow for improved interpretations of the data to enhance the knowledge and the predictive capabilities of the flow system. This work thoroughly reanalyzes a series of preand post-hydraulic fracturing, single-well aquif...

The derivative of an ideal in a number ring is defined and the relation between the ideal derivative and the arithmetic derivative of a number in Z is discussed. Some simple ideal di↵erential equations are also studied. Further, the definition of the ideal derivative is extended to the derivative of a fractional ideal in a number ring. Again, the relation between the fractional ideal derivative...