Sharif Digital Repository

Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For this purpose we use the Bismut local index formula in the context of noncommutative geometry. This paper uses heavily the methods and technical results developed by E. Leichtnam and P. Piazza  

In this short note we apply methods introduced by B. Hanke and T. Schick to prove the vanishing of (low degree) higher Â-genera for spin manifolds admitting a positive scalar curvature metric. Our aim is to provide a short proof for this beautiful result  

Let Γ = (G, σ) be a signed graph, where G is the underlying simple graph and σ E(G) → {-, +} is the sign function on the edges of G. The adjacency matrix of a signed graph has-1 or +1 for adjacent vertices, depending on the sign of the edges. It was conjectured that if is a signed complete graph of order n with k negative edges, k-lt-n-1 and has maximum index, then negative edges form K1 ,k. In this paper, we prove this conjecture if we confine ourselves to all signed complete graphs of order n whose negative edges form a tree of order k + 1. A [1, 2]-subgraph of G is a graph whose components are paths and cycles. Let Γ be a signed complete graph whose negative edges form a [1, 2]-subgraph.... 

In this paper we show how the higher index theory can be used to prove results concerning the non-existence of a complete Riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods to prove such non-existence theorems  

The ABC index is a topological index was defined as where dG(u) denotes degree of vertex u. Now we define a new version of ABC index as where The goal of this paper is further the study of the ABC4 index  

The Zagreb indices have been introduced more than thirty years ago by Gutman and Trinajstić. In this paper we introduce a new version of Zagreb indices and then we compute them for an infinite family of nanostar dendrimers  

One of the key solutions to improve engine performance and reduce exhaust emissions of internal combustion engines is direct injection of bio-fuels. A new modified bio-ethanol is produced to be substituted by fossil fuels in gasoline direct injection engines. The key advantages of modified bio-ethanol fuel as an alternative fuel are higher octane number and oxygen content, a long-chain hydro-carbon fuel, and lower emissions compared to fossil fuels. In the present study spray properties of a modified bio-ethanol and its atomization behaviors have been studied experimentally and theoretically. Based on atomization physics of droplets dimensional analysis has been performed to develop a new... 

Let G be a simple graph with n vertices and let λ1, λ2,...,λn be its eigenvalues. The energy of G is defined to be E(G) = ∑i=1n|λi|. In this note, for a given k-regular graph we find explicit formulas for the energy of L(G), the complement of line graph of G. This provides us with some practical ways to compute the energy of a large family of regular graphs  

The energy E of any n-vertex regular graph G of degree r, r > 0, is greater than or equal to n. Equality holds if and only if every component of G is isomorphic to the complete bipartite graph Kr,r. If G is triangle- and quadrangle-free, then E ≥ nr/√2r - 1. In particular, for any fullerene and nanotube with n carbon atoms, 1.34n ≤ E ≤ 1.73 n  

It seems that the index theory for non-compact spaces has found its ultimate formulation in the realm of coarse spaces and K-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and interesting examples of this program. In this paper we formulate a combination of these two theorems and establish a partitioned-relative index theorem. © 2019 Elsevier Masson SAS  

One of the significant challenges in urbanization is the air pollution. This highlights the need of the green city concept with reconsideration of houses, factories, and traffic in a green viewpoint. The literature review confirms that this reconsideration for green space has a positive effect on the air quality of large cities and to reduce the air pollution. The purpose of this study is to evaluate the annual vegetation changes in the green space of Mashhad, Iran as a very populated city in the middle east to study the air pollution. To investigate the relationship between the air pollution and vegetation, the Landsat 8 satellite images for summer seasons of 2013–2019 were used to extract... 

Some new relations have been established between Wiener indices, stability numbers and clique numbers for several classes of composite graphs that arise via graph products. For three of considered operations we show that they make a multiplicative pair with the clique number  

Let G be a graph. The core of G, denoted by G Δ, is the subgraph of G induced by the vertices of degree Δ(G), where Δ(G) denotes the maximum degree of G. A k-edge coloring of G is a function f: E(G) → L such that |L| = k and f (e 1) ≠ f (e 2) for all two adjacent edges e 1 and e 2 of G. The chromatic index of G, denoted by χ′(G), is the minimum number k for which G has a k-edge coloring. A graph G is said to be Class 1 if χ′(G) = Δ(G) and Class 2 if χ′(G) = Δ(G) + 1. In this paper it is shown that every connected graph G of even order and with Δ(G Δ) ≤ 2 is Class 1 if |G Δ| ≤ 9 or G Δ is a cycle of order 10  

In this work, we study the problem of linear index coding from graph homomorphism point of view. We show that the decision version of linear (scalar or vector) index coding problem is equivalent to certain graph homomorphism problem. Using this equivalence expression, we conclude the following results. First we introduce new lower bounds on linear index of graphs. Next, we show that if the linear index of a graph over a finite filed is bounded by a constant, then by changing the ground field, the linear index of the graph may change by at most a constant factor that is independent from the size of the graph. Finally, we show that the decision version of linear index coding problem is... 

Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this article, the basic properties of G(R) are investigated and some characterization results regarding connectedness, chromatic index, diameter, girth, and planarity of G(R)are given. (These terms are defined in Definitions and Remarks 4.1, 5.1, 5.3, 5.9, and 5.13.)  

Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a Hermitean bundle on M with connection. We define a coarse multi-partitioned index of the spin Dirac operator on M twisted by E. Our main result is the computation of this multi-partitioned index as the Fredholm index of the Dirac operator on the compact manifold N, twisted by the restriction of E to N. We establish the following main application: if the scalar curvature of M is bounded below by a positive constant everywhere (or even if this happens only on one of... 

4E analysis is used on a Brayton-Rankine combined cycle power plant (CCPP) with a dual pressure heat recovery steam generation (HRSG) system. A multi-objective genetic-based evolutionary optimization has been used to estimate the most optimal exergy efficiency status, exergy cost reduction, carbon emission reduction, and NOx emission reduction. For the validation of the data, the simulation results are compared with the plant's data. This study investigates the effect of every decisive parameter on the objective performance parameters of the CCPP. The primary estimated results are the emission rates, efficiencies, and the exergoeconomic cost of the system. At the optimum operational state,... 

An integrated probabilistic framework is proposed with a set of probabilistic models that are compatible with the reliability methods used in resilience-based design (RBD). Previous seismic resilience estimation frameworks primarily have used conditional probabilities and total probability integration to compute the expected seismic resilience index while considering the effects of only a few types of uncertainty. However, a high level of uncertainty is associated with seismic resilience estimation. This study presents a probabilistic framework and models that can consider the effect of unlimited uncertainties when calculating the probability distribution of the seismic resilience index for... 

In this paper the fabrication, testing and results of inverse profiling of optical slab waveguides in glass are reported. This is the first successful report of fabricating ion exchange optical waveguides in Iran. © Shiraz University  

The growth of process industries has escalated the probability of loss containment scenarios of hazardous materials that can be tackled via process safety schemes. For preliminary design stage, the inherent scheme is more promising to generate sustainable process designs. For this purpose, various process routes are typically compared to recognize the safer one via numerous indexing methods to eliminate routes with hazardous materials. However, these indices lack in accommodating the equipment characteristics and the underutilization of process and chemical characteristics. Specifically for chemical characteristics, the toxicity aspect has not been engaged for process route selection in...