Narrow Results

We show that any proper rigid analytic surface admits a relatively minimal regular model. Further, we give a criterion for relative minimality of proper regular rigid analytic surfaces.

We construct examples of $n$-folds of general type with relatively small volumes with respect to $p_g(X)$.

We present a minimal regulatory model for the dynamics of the humoral immune response of two lymphocytes populations (B and T helper) interacting with a specific antigen pool (bacterium). Stability analysis reveals that the system accounts for the occurrence of multiple steady states in the absence as well as in the presence of the antigen population. The model exhibits (i) a state of immune memory, (ii) one state with high antigen and low helper concentration (disease), and (iii) one state with low antigen and high helper concentration (tolerance). The latter state allows oscillatory behavior. Injection of high antigen doses as well as minimal changes of structural parameters provoke the system to jump from the state of disease to the state of tolerance. This is reminiscent of therapies where the patient is treated with allergen, immuno-suppressants or drugs.

COVID-19 pandemic is one of the major disasters that humanity has ever faced. In this paper, we try to model the effect of vaccination in controlling the pandemic, particularly in context to the third wave which is predicted to hit globally. Here, we have modified the susceptible–exposed–infected–recovered–dead model by introducing a vaccination term. One of our main assumptions is that the infection rate ($\beta (t)$) is oscillatory. This oscillatory nature has been discussed earlier in literature with reference to the seasonality of epidemics. However, in our case, we invoke this nature of the infection rate ($\beta (t)$) to model the cyclical behavior of the COVID-19 pandemic within a short period. This study focuses on a minimalistic approach where we have logically deduced that the infection rate ($\beta (t)$) and the vaccination rate ($\lambda$) are the most important parameters while the other parameters can be assumed to be constants throughout the simulation. Finally, we have studied the rich interplay between the infection rate ($\beta (t)$) and the vaccination rate ($\lambda$) on the infectious cases of COVID-19 and made some robust conclusions regarding the global behavior of this pandemic in near future.

We demonstrate using two examples that a minimal model of a spin system can present qualitative correct magnetization plateaus which are almost the same as the original model. Some arguments on the generality of the minimal model approach are given. The approach can serve as a primary approximation and a assistance to the analytical and numerical methods.

In this paper we describe the paraconsistent circumscription by the application of predicate circumscription in a paraconsistent logic, the logic of paradox LP. In addition to circumscribing the predicates, we also circumscribe the inconsistency. The paraconsistent circumscription can be well characterized by the minimal semantics which is both nonmonotonic and paraconsistent. It brings us advantages in two respects: nonmonotonic logic would be nontrivial while there was a contradiction, and paraconsistent logic would be equivalent to classical logic while there was no effect of a contradiction.

A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.

For a space, we investigate its CJL (cohomology jump loci), sitting inside varieties of representations of the fundamental group. To do this, for a CDG (commutative differential graded) algebra, we define its CJL, sitting inside varieties of flat connections. The analytic germs at the origin 1 of representation varieties are shown to be determined by the Sullivan 1-minimal model of the space. Up to a degree q, the two types of CJL have the same analytic germs at the origins, when the space and the algebra have the same q-minimal model. We apply this general approach to formal spaces (obtaining the degeneration of the Farber–Novikov spectral sequence), quasi-projective manifolds, and finitely generated nilpotent groups. When the CDG algebra has positive weights, we elucidate some of the structure of (rank one complex) topological and algebraic CJL: all their irreducible components passing through the origin are connected affine subtori, respectively rational linear subspaces. Furthermore, the global exponential map sends all algebraic CJL into their topological counterpart.

In this paper, we present a modified minimal model for glucose and insulin kinetics model. The model proposed here is a smooth approximation of the original non-smooth minimal model. The dynamical properties like dissipativity, existence of equilibrium and stability of the system at the equilibrium points are investigated. A linear feedback-based control strategy is studied to control the blood glucose level in the situation where the physical system fails to regulate the blood glucose level automatically. A critical control parameter value $k_c$ is determined in terms of the system parameters. Extensive numerical simulation is performed with different parameter sets. Assuming different values for the feedback gain parameter, ranges of physiological parameter $\alpha$ are determined where the feedback gain is sufficient to stabilize the control system.

In our research work, we suggest the modified minimal model of fractional order and analyze it using the homotopy decomposition method (HDM). The minimal model is quite a useful mathematical model which describes the behavior of glucose-insulin metabolism. The original model was given in the 80s and has been updated over a different period. In this modified model, we add a one-factor diet which plays an important role in the blood-glucose analysis. We obtained the numerical results by using the homotopy decomposition method. HDM is extremely useful, significant, and very simple. We also discuss the existence and uniqueness of the fractional model.