New bounds on the signed total domination number of graphs

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turan, we present a sharp lower bound on this parameter for graphs with no complete graph of order r+1 as a subgraph. Also, we prove that n-2(s-s') is an upper bound on the signed total domination number of any tree of order n with s support vertices and s' support vertives of degree two. Moreover, we characterize all trees attainig this bound.Comment: This paper contains 11 pages and one figur

On the inverse signed total domination number in graphs

In this paper, we study the inverse signed total domination number in graphs and present new lower and upper bounds on this parameter. For example by making use of the classic theorem of Turan (1941), we present a sharp upper bound for graphs with no induced complete subgraph of order greater than two. Also, we bound this parameter for a tree in terms of its order and the number of leaves and characterize all trees attaining this bound

Energy Gap from Step Structure of the Analytically Inverted Non-Additive Kinetic Potential

The bandgap constitutes a challenging problem in density functional theory (DFT) methodologies. It is known that the energy gap values calculated by common DFT approaches are underestimated. The bandgap was also found to be related to the derivative discontinuity (DD) of the exchange-correlation potential in the Kohn-Sham formulation of DFT. Several reports have shown that DD appears as a step on the potential curve. The step structure is a mandatory structure for aligning the KS energy levels in the ionization potentials in a dissociated molecule in both fragments and is a function of electron localisation. Reproducing the step in the DFT framework gives the charge transfer process and the correct energy gap and describes the source of dissociation. This step phenomenon has not yet been studied in the non-additive kinetic potential $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$, a key quantity used in embedding theories. While $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$ is known to be difficult to approximate, in this work, we explain how an accurate energy gap can be produced from the analytically inverted $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$, even if we use the input densities calculated by the local and semi-local functionals. We used the precisely calculated $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$ reported in our previous publication [Phys. Rev. A 106, 042812 (2022)] to produce the energy gap for some model systems and report in this work the promising accuracy of our results through the comparison with the results obtained from one of the most accurate calculations, OEP theory with the KLI local approximation.Comment: 33 pages, 18 figure

In Pursuit of Sustainable Strategic Long-term Planning Throughout Meta-postmodernism as New Perspective of Stylistic Design

During the different period of architectural design, designers attempt to achieve high level of life quality for all users. Architecture and urban planner want to provide a style of design which not only achieves different function for different users with respect to their ethnicity, ability, age, sex, capability, position, and life style but also improve friendly environment throughout responsive legislation based on long-term planning. Although, the styles are considered some indicators, it is ignored the other important characteristics. Therefore, the existing styles never achieve standard level of satisfaction of different people. The goal of the research is to introduce meta-postmodern style as supplement stylistic approach. The style tries to consider all important indicators that create a strategic long-term planning for different generations. Various characteristics of new style can be applied to improve the quality of human life and provide a health, livable and sustainable planning for all users

On the Signed 22-independence Number of Graphs

In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach. In this way, we can improve and generalize some known results in this area

Modeling Wettability Alteration using Chemical EOR Processes in Naturally Fractured Reservoirs

The objective of our search is to develop a mechanistic simulation tool by adapting UTCHEM to model the wettability alteration in both conventional and naturally fractured reservoirs. This will be a unique simulator that can model surfactant floods in naturally fractured reservoir with coupling of wettability effects on relative permeabilities, capillary pressure, and capillary desaturation curves. The capability of wettability alteration will help us and others to better understand and predict the oil recovery mechanisms as a function of wettability in naturally fractured reservoirs. The lack of a reliable simulator for wettability alteration means that either the concept that has already been proven to be effective in the laboratory scale may never be applied commercially to increase oil production or the process must be tested in the field by trial and error and at large expense in time and money. The objective of Task 1 is to perform a literature survey to compile published data on relative permeability, capillary pressure, dispersion, interfacial tension, and capillary desaturation curve as a function of wettability to aid in the development of petrophysical property models as a function of wettability. The new models and correlations will be tested against published data. The models will then be implemented in the compositional chemical flooding reservoir simulator, UTCHEM. The objective of Task 2 is to understand the mechanisms and develop a correlation for the degree of wettability alteration based on published data. The objective of Task 3 is to validate the models and implementation against published data and to perform 3-D field-scale simulations to evaluate the impact of uncertainties in the fracture and matrix properties on surfactant alkaline and hot water floods