Ali Parsian - Academia.edu (original) (raw)

Papers by Ali Parsian

Communications in algebra, May 29, 2024

International Journal of Mathematics and Mathematical Sciences, 1999

For a real Hilbert space (H, ,), a subspace L ⊂ H ⊕ H is said to be a Dirac structure on H if it ... more For a real Hilbert space (H, ,), a subspace L ⊂ H ⊕ H is said to be a Dirac structure on H if it is maximally isotropic with respect to the pairing (x, y), (x ,y) + = (1/2)(x, y + x ,y). By investigating some basic properties of these structures, it is shown that Dirac structures on H are in one-to-one correspondence with isometries on H, and, any two Dirac structures are isometric. It is, also, proved that any Dirac structure on a smooth manifold in the sense of [1] yields a Dirac structure on some Hilbert space. The graph of any densely defined skew symmetric linear operator on a Hilbert space is, also, shown to be a Dirac structure. For a Dirac structure L on H, every z ∈ H is uniquely decomposed as z = p 1 (l) + p 2 (l) for some l ∈ L, where p 1 and p 2 are projections. When p 1 (L) is closed, for any Hilbert subspace W ⊂ H, an induced Dirac structure on W is introduced. The latter concept has also been generalized.

Journal of Fundamental and Applied Sciences, 2016

Newton's laws of motion are three physical laws that together, laid the foundation for classi... more Newton's laws of motion are three physical laws that together, laid the foundation for classical three dimensional mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. Kepler's laws of planetary motion are also three scientific laws describing the motion of planets around the Sun. Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a non uniform field of force by small steps. Even though neither the force was known nor its relation to motion, he could determine the differential equations of motion from observation. This is one of the most important achievements in the history of physics. In this paper, we will see that these laws are a consequence of Newton’s second law even in multidimensional Euclidian spaces.

Match Communications in Mathematical and in Computer Chemistry

As a novel member of the class of vertex-degree-based topological indices, the so-called Sombor i... more As a novel member of the class of vertex-degree-based topological indices, the so-called Sombor index was recently introduced by Gutman on the chemical graphs. In this paper, we present the minimum Sombor index for unicyclic graphs with the diameter D>_2.

Ferdowsi University

Extended Abstracts of the 16th Seminar on Math. Anal. Appl. 4-5 February 2007, Ferdowsi Universit... more Extended Abstracts of the 16th Seminar on Math. Anal. Appl. 4-5 February 2007, Ferdowsi University, Mashhad, pp. 109112 APPLICATIONS OF MAXIMALITY IN THE DECOMPOSITION OF HILBERT SPACES ALI PARSIAN Abstract. The Closed subsets of Hilbert spaces have ...

In this paper we are supposed to define the θ−vector field on the n−surface S and then investigat... more In this paper we are supposed to define the θ−vector field on the n−surface S and then investigate about the existence and uniqueness of its integral curves by the Theory of Ordinary Differential Equations. Then the subject is followed through some examples.

Journal of Linear and Topological Algebra, 2018

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and p... more ‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on Rn(ngeq1)R^{n} (ngeq 1)Rn(ngeq1)‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some applications‎. .

Turkish Journal of Mathematics, 2021

Nowadays, traditional methods of education, in particular in mathematics education, do not reply ... more Nowadays, traditional methods of education, in particular in mathematics education, do not reply all required educational needs, and intelligent educational methods play a sensitive role in easy studying and understanding mathematics. But, lack of necessary facilities in some outlying schools, disinterestedness or debility of some teachers on learning new methods in education, are among some problems that make using these methods impossible. In this research, a new method for education, independent of the existing intelligence ones, especially in mathematics, is introduced. Then it has been exerted on two different groups of students at two different bases in one of the frontier provinces in Iran. Then the results are compared through inferential statistical methods with another two groups at same bases that have been educated with usually scholastic methods. Using statistical analysis shows that mathematics education through the introduced method has a competent role on amendment o...

Let G=(V,E)G=(V,E)G=(V,E) be a simple graph with vertex set V=V(G)V=V(G)V=V(G) and edge set E=E(G)E=E(G)E=E(G). A Roman dominatin... more Let G=(V,E)G=(V,E)G=(V,E) be a simple graph with vertex set V=V(G)V=V(G)V=V(G) and edge set E=E(G)E=E(G)E=E(G). A Roman dominating function (RDF) on a graph GGG is a function f:Vrightarrow0,1,2f:V\rightarrow\{0,1,2\}f:Vrightarrow0,1,2 satisfying the condition that every vertex uuu for which f(u)=0f(u)=0f(u)=0 is adjacent to at least one vertex vvv such that f(v)=2f(v)=2f(v)=2. The weight of fff is omega(f)=SigmavinVf(v)\omega(f)=\Sigma_{v\in V}f(v)omega(f)=SigmavinVf(v). The minimum weight of an RDF on GGG, gammaR(G)\gamma_{R}(G)gammaR(G), is called the Roman domination number of GGG. gammaR(G)leq2gamma(G)\gamma_{R}(G)\leq 2\gamma(G)gammaR(G)leq2gamma(G) where gamma(G)\gamma(G)gamma(G) denotes the domination number of GGG. A graph GGG is called a Roman graph whenever gammaR(G)=2gamma(G)\gamma_{R}(G)= 2\gamma(G)gammaR(G)=2gamma(G). On the other hand, the differential of XXX is defined as partial(X)=∣B(X)∣−∣X∣\partial(X)=|B(X)|-|X|partial(X)=∣B(X)∣−∣X∣ and the differential of a graph GGG, written partial(G)\partial(G)partial(G), is equal to maxpartial(X):XsubseteqVmax\{\partial(X): X\subseteq V\}maxpartial(X):XsubseteqV. By using differential we provide a sufficient and necessary condition for the graphs to be Roman. We also modify the proof of a result on Roman trees. Finally we characterize the large family of tre...

Let A be a symmetric positive definite (n+1)×(n+1) real matrix for n ≥ 1 and S ∈ R be a hypersurf... more Let A be a symmetric positive definite (n+1)×(n+1) real matrix for n ≥ 1 and S ∈ R be a hypersurface. We are supposed to determine the tangent space TpS in an arbitrary point p ∈ S in the case that the whole space R admits the inner product with matrix A. Among other things, some maximum and minimum properties for the vector fields perpendicular to tangent spaces of hypersurfaces, the compatibility of the image or inverse image of a hypersurface and its tangent space under an embedding, an isometry, and a submersion are also pointed out.

Let G=(V,E)G=(V,E)G=(V,E) be a simple graph with vertex set V=V(G)V=V(G)V=V(G), edge set E=E(G)E=E(G)E=E(G) and from maximum deg... more Let G=(V,E)G=(V,E)G=(V,E) be a simple graph with vertex set V=V(G)V=V(G)V=V(G), edge set E=E(G)E=E(G)E=E(G) and from maximum degree Delta=Delta(G)\Delta=\Delta(G)Delta=Delta(G). Also let f:Vrightarrow0,1,...,lceilfracDelta2rceil+1f:V\rightarrow\{0,1,...,\lceil\frac{\Delta}{2}\rceil+1\}f:Vrightarrow0,1,...,lceilfracDelta2rceil+1 be a function that labels the vertices of GGG. Let Vi=vinV:f(v)=iV_i=\{v\in V: f(v)=i\}Vi=vinV:f(v)=i for i=0,1i=0,1i=0,1 and let V2=V−(V0bigcupV1)=winV:f(w)geq2V_2=V-(V_0\bigcup V_1)=\{w\in V: f(w)\geq2\}V2=V−(V0bigcupV1)=winV:f(w)geq2. A function fff is called a strong Roman dominating function (StRDF) for GGG, if every vinV0v\in V_0vinV0 has a neighbor www, such that winV2w\in V_2winV2 and f(w)geq1+lceilfrac12∣N(w)bigcapV0∣rceilf(w)\geq 1+\lceil\frac{1}{2}|N(w)\bigcap V_0|\rceilf(w)geq1+lceilfrac12∣N(w)bigcapV0∣rceil. The minimum weight, omega(f)=f(V)=SigmavinVf(v)\omega(f)=f(V)=\Sigma_{v\in V} f(v)omega(f)=f(V)=SigmavinVf(v), over all the strong Roman dominating functions of GGG, is called the strong Roman domination number of GGG and we denote it by gammaStR(G)\gamma_{StR}(G)gammaStR(G). An StRDF of minimum weight is called a gammaStR(G)\gamma_{StR}(G)gammaStR(G)-function. Let overlineG\overline{G}overlineG be the complement of GGG. The complementary prism GoverlineGG\overline{G}GoverlineG of GGG is the graph formed from the disjoint union GGG and overlineG\overline{G}overlineG by adding the edges of a perfect mat...

Devising the methods for transferring the information confidentially is very important and plays ... more Devising the methods for transferring the information confidentially is very important and plays a sensitive role in the human communities. Sending cryptic information is one of the methods which can be used for this aim. In this paper, pointed to some available cryptographic systems such as DNA molecule, the probability of random breaking of some of them is found. Then some new encryption techniques are provided. In the next, by finding the probability of random breaking the cipher texts with recommended methods it is shown that each of them, have been formulated in order to enhance the security of the encryption systems. As a result we see that the probability of random breaking the cipher texts with recommended methods will be decreased at a rate between 1.18 ∙ 10 −37 and 2.87 ∙ 10 −6 times.

Biomedical Research-tokyo, 2017

Melanoma is one of the most dangerous tumors in the human kind cancers. Nonetheless, early detect... more Melanoma is one of the most dangerous tumors in the human kind cancers. Nonetheless, early detection of this cancer can help the doctors to cure it perfectly. In this paper, a new efficient method is proposed to detect the malignant melanoma images from the images. In the proposed method, a hybrid technique is utilized. We first eliminate the extra scales by using edge detection and smoothing. Afterwards, the main hybrid technique is applied to segment the cancer images. Finally by using the morphological operations, the extra information is eliminated and used to focus on the area which melanoma boundary potentially exists. Here, Gray Wolf Optimization algorithm is utilized to optimize an MLP neural Networks (ANN). Gray Wolf Optimization is a new evolutionary algorithm which recently introduced and has a good performance in some optimization problems. GWO is a derivative-free, Meta Heuristic algorithm, mimicking the ecological behaviour of colonizing weeds. Gray wolf optimization i...

Controlling the population necessitates attention to all of its effective factors. This care must... more Controlling the population necessitates attention to all of its effective factors. This care must have harmony to the real life. Modifying the beliefs of peoples is one of the various techniques that can be affected on this phenomenon. In this study, by a mathematical model using probability theory, the effects of some cultural beliefs of the peoples about the number of boys' children, in the growth of their population are investigated. Then by using the results of the model and Verhulst equation, a limiting number of populations with respect to their rates of collaboration and competition will be indicated. Finally, through the theory of ordinary differential equations, a general formula for this limit will be presented.

Electronic Journal of Graph Theory and Applications

Given a simple graph G = (V, E) with maximum degree ∆. Let (V 0 , V 1 , V 2) be an ordered partit... more Given a simple graph G = (V, E) with maximum degree ∆. Let (V 0 , V 1 , V 2) be an ordered partition of V , where V i = {v ∈ V : f (v) = i} for i = 0, 1 and V 2 = {v ∈ V : f (v) ≥ 2}. A function f : V → {0, 1,. .. , ∆ 2 +1} is a strong Roman dominating function (StRDF) on G, if every v ∈ V 0 has a neighbor w ∈ V 2 and f (w) ≥ 1 + 1 2 |N (w) ∩ V 0 |. A function f : V → {0, 1,. .. , ∆ 2 + 1} is a unique response strong Roman function (URStRF), if w ∈ V 0 , then |N (w) ∩ V 2 | ≤ 1 and w ∈ V 1 ∪ V 2 implies that |N (w) ∩ V 2 | = 0. A function f : V → {0, 1,. .. , ∆ 2 + 1} is a unique response strong Roman dominating function (URStRDF) if it is both URStRF and StRDF. The unique response strong Roman domination number of G, denoted by u StR (G), is the minimum weight of a unique response strong Roman dominating function. In this paper we approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, for any tree T of order n ≥ 3 we prove the sharp bound u StR (T) ≤ 8n 9 .

Iranian Journal of Science and Technology, Transactions A: Science

In the present paper, we introduce the concept of a slant vector field \chi$$χ defined on a hyp... more In the present paper, we introduce the concept of a slant vector field \chi$$χ defined on a hypersurface S, as a generalization of the tangent vector field on S, and investigate the problem of its existence, uniqueness and integral curve. Among other things, we provide an integral equation and also a differential equation for the integral curve of \chi$$χ, say \alpha$$α, defined on an open interval I containing 0 such that \alpha (0)=p$$α(0)=p, where p is an arbitrary point of the hypersurface. At the end, we also investigate some special cases and some examples.

International Journal of Applied Mathematical Research, 2016

Let $S$ be a nonempty set and $F$ consists of all $Z_{2}$ characteristic functions defined ... more Let $S$ be a nonempty set and $F$ consists of all $Z_{2}$ characteristic functions defined on $S$. We are supposed to introduce a ring isomorphic to $(P(S),\triangle,\cap)$, whose set is $F$. Then, assuming a finitely additive function mmm defined on $P(S)$, we change $P(S)$ to a pseudometric space $(P(S),d_{m})$ in which its pseudometric is defined by $m$. Among other things, we investigate the concepts of convergence and continuity in the induced pseudometric space. Moreover, a theorem on the measure of some kinds of elements in $(P(S),m)$ will be established. At the end, as an application in probability theory, the probability of some events in the space of permutations with uniform probability will be determined. Some illustrative examples are included to show the usefulness and applicability of results.

THE ISLAMIC SCIENCE QUARTERLY, 2010

Historians have always emphasized the magnificent past era of Islamic Empire, the dominion of mus... more Historians have always emphasized the magnificent past era of Islamic Empire, the dominion of muslim civilization and the fame of muslim scholars. The creation of a novel scientific and global civilization during two centuries is really extraordinary. These ...