General properties of exchange rate of national money versus some foreign currencies in Albania

In this work we have considered the study of the exchange rate series for the specific case where the formal financial market is not active. In those situations, we would be interested in the parallelization of the exchange rate with financial indexes for stabilized financial market. We observed that the stationarity of the distribution for some the exchange rate of currencies traded in the country differs significantly. The time dynamics shows the presence of the elements of local critical behavior, but those tendencies attenuate and fade away in an a periodic fashion. Next, we considered and evidenced the correlation distances and dissimilarity between exchange rates of national currencies versus euro and dollar and golden prices. It resulted that two exchange rates do have different distance from golden price taken for references. The correlation distance between the series of the return in different period has evidenced that there is not a regular behavior in this respect.

Seshadri constants on principally polarized abelian surfaces with real multiplication

Seshadri constants on abelian surfaces are fully understood in the case of Picard number one. Little is known so far for simple abelian surfaces of higher Picard number. In this paper we investigate principally polarized abelian surfaces with real multiplication. They are of Picard number two and might be considered the next natural case to be studied. The challenge is to not only determine the Seshadri constants of individual line bundles, but to understand the whole Seshadri function on these surfaces. Our results show on the one hand that this function is surprisingly complex: on surfaces with real multiplication in $$\mathbb {Z}[\sqrt{e}]$$ Z [ e ] it consists of linear segments that are never adjacent to each other—it behaves like the Cantor function. On the other hand, we prove that the Seshadri function is invariant under an infinite group of automorphisms, which shows that it does have interesting regular behavior globally.

Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation

In this paper, the dynamics of a 3D autonomous dissipative nonlinear system of ODEs-Rössler prototype-4 system, was investigated. Using Lyapunov-Andronov theory, we obtain a new analytical formula for the first Lyapunov’s (focal) value at the boundary of stability of the corresponding equilibrium state. On the other hand, the global analysis reveals that the system may exhibit the phenomena of Shilnikov chaos. Further, it is shown via analytical calculations that the considered system can be presented in the form of a linear oscillator with one nonlinear automatic regulator. Finally, it is found that for some new combinations of parameters, the system demonstrates chaotic behavior and transition from chaos to regular behavior is realized through inverse period-doubling bifurcations.

Semantic Filtering of Twitter Data Using Labeled Property Graph (LPG)

Hidden interests of an individual can be inferred by keenly observing their social profile data and blending this data with a semantic network. Getting user interests without user’s manual intervention is very beneficial for companies feeding on user’s regular behavior. This paper provides the entire idea of how to retrieve the user’s hidden interests and what is a semantic network. Twitter is the preferred social platform for entities extraction. We started basically by gathering entities like hashtags and keywords from the tweets posted by an individual. And simultaneously created a Semantic Network using Wikipedia’s taxonomy of categories and subcategories and pages implementing a concept called Labeled Property Graph (LPG). Matching the pre-obtained tweet entities with the Wikipedia graph of Categories and Pages a graph is generated called Hierarchical Interest Graph (HIG) which contains so called hidden interests of user. HIG of an individual is an isolated entity and may never match with others’ HIG.

Many-dimensional tauberian theorems for holomorphic functions of bounded argument

For generalized functions with Laplace transform has nonnegative imaginary part in tube domain over positive actant, we found sufficient conditions for existence of quasiasymptotic, the function with regular behavior with respect to which the quasiasymptotic exists being explicitly found. The obtained results are used to steady of the asymptotic behaviour of solutions of the Cauchy problem of passive operators.

Regularizations of time-crystal dynamics

We demonstrate that nonconvex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise in the reduced description. Microstructure featuring intervals of fixed velocity interrupted by quick resets—“Sisyphus dynamics”—is a generic consequence. In quantum mechanics, this microstructure can be blurred, leaving entirely regular behavior.