In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

There are two basic types of improper integrals. Integrals with an infinite limit are defined as the limit of a series of proper integrals as one of the limits approaches infinity. Improper integrals with finite limits are needed when the integrand does not have a finite limiting value as the variable of integration approaches a particular “critical” value. In this case, the improper integral i...

The usual E, δ-definition of the limit of a function (whether pre­ sented at a rigorous or an intuitive level) requires a “candidate L” for the limit value. Thus, we have to start our first calculus course with “guessing” instead of “calculating”. In this paper we criticize the method of using calculators for the purpose of selecting candidates for L. We suggest an alternative: a working formul...

in [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.also, we exhibited the topic of limit summability of real functions in [2,3]. inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. finally, we pose an unsolved problem aboutthem.

this paper is devoted to the study of determining optimal process mean in system production with the two markets for the sale of goods. in this paper, we developed an absorbing markov chain model in production systems where all items are inspected %100 for conformance with their specification limits. when the value of the quality characteristic of an item falls below a lower limit, the item is ...

Road transport is a ubiquitous source of lead contamination in the soil near highways with direct and indirect impacts on human health. Accumulation of traffic-induced lead in the soils depends on gasoline lead content, traffic volume, as well as meteorological conditions. To evaluate the effect of traffic on soil lead concentration, 113 samples from the topsoil (0-15 cm) were collected in a re...

in this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.

this paper considers the problem of stable limit cycles generating in a class of uncertain nonlinear systems which leads to stable oscillations in the system’s output.this is a wanted behavior in many practical engineering problems. for this purpose, first the equation of the desirable limit cycle is achieved according to shape, amplitude and frequency of the required output oscillations. then,...

a label-free electrochemical nucleic acid aptasensor for the detection of methamphetamine (ma) by the immobilization of thiolated self-assembled dna sequences on a gold nanoparticles-chitosan modified electrode is constructed. when ma was complexed specifically to the aptamer, the configuration of the nucleic acid aptamer switched to a locked structure and the interface of the biosensor changed...