Search results for: split graphs

Authors: Ivan Belik

Abstract:

In terms of social networks split graphs correspond to the variety of interpersonal and intergroup relations. In this paper we analyse the interaction between the cliques (socially strong and trusty groups) and the independent sets (fragmented and non-connected groups of people) as the basic components of any split graph. Based on the Semi-Lagrangean relaxation for the k-cardinality assignment problem we show the way of how to minimize the socially risky interactions between the cliques and the independent sets within the social network.

Keywords: cliques, independent sets, k-cardinality assignment, social networks, split graphs

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Authors: Gete Umbrey, Saifur Rahman

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Graphs are found to be most capable in computing, and its abstract structures have been applied in some specific computations and algorithms like in phase encoding controller, processor microcontroller, and synthesis of a CMOS switching network, etc. Being motivated by these works, we develop an independent approach to study semiring structures and various properties by defining the binary operations which in fact, seems analogous to an existing definition in some sense but with a different approach. This work emphasizes specifically on the construction of semigroup and semiring structures on the set of undirected graphs, and their properties are investigated therein. It is expected that the investigation done here may have some interesting applications in theoretical computer science, networking and decision making, and also on joining of two network systems.

Keywords: graphs, join and union of graphs, semiring, weighted graphs

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Authors: Seyed Ahmad Mojallal

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Let G be a connected threshold graph of order n with m edges and trace T. In this talk we give a lower bound on Laplacian energy in terms of n, m, and T of G. From this we determine the threshold graphs with the first four minimal Laplacian energies. We also list the first 20 minimal Laplacian energies among threshold graphs. Let σ=σ(G) be the number of Laplacian eigenvalues greater than or equal to average degree of graph G. Using this concept, we obtain the threshold graphs with the largest and the second largest Laplacian energies.

Keywords: Laplacian eigenvalues, Laplacian energy, threshold graphs, extremal graphs

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Authors: Y. Wang

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The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Swapnil Gupta, C. Pandu Rangan

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A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: uniquely restricted matching, interval graph, matching, induced matching, witness counting

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Authors: Vadim E. Levit, Eugen Mandrescu

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A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered.

Keywords: maximum independent set, corona, concatenation, join, well-covered graph

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Authors: Robert Gold

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Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modelled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyse the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: control flow graph, graph reduction, software engineering, software applications

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Authors: Khidir R. Sharaf, Didar A. Ali

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The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: graph theory, graph spectra, nullity of graphs, statistic

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Authors: Sofia Ait Bouazza

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We consider the problem of finding a minimum identifying code in a graph. This problem was initially introduced in 1998 and has been since fundamentally connected to a wide range of applications (fault diagnosis, location detection …). Suppose we have a building into which we need to place fire alarms. Suppose each alarm is designed so that it can detect any fire that starts either in the room in which it is located or in any room that shares a doorway with the room. We want to detect any fire that may occur or use the alarms which are sounding to not only to not only detect any fire but be able to tell exactly where the fire is located in the building. For reasons of cost, we want to use as few alarms as necessary. The first problem involves finding a minimum domination set of a graph. If the alarms are three state alarms capable of distinguishing between a fire in the same room as the alarm and a fire in an adjacent room, we are trying to find a minimum locating domination set. If the alarms are two state alarms that can only sound if there is a fire somewhere nearby, we are looking for a differentiating domination set of a graph. These three areas are the subject of much active research; we primarily focus on the third problem. An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most r≥1 from x. When only vertices out of the code are asked to be identified, we get the related concept of a locating dominating set. The problem of finding an identifying code (resp a locating dominating code) of minimum size is a NP-hard problem, even when the input graph belongs to a number of specific graph classes. Therefore, we study this problem in some restricted classes of undirected graphs like split graph, line graph and path in a directed graph. Then we present some results on the identifying code by giving an exact value of upper total locating domination and a total 2-identifying code in directed and undirected graph. Moreover we determine exact values of locating dominating code and edge identifying code of thin headless spider and locating dominating code of complete suns.

Keywords: identiying codes, locating dominating set, split graphs, thin headless spider

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Authors: S. R. Nayaka, Putta Swamy

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Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

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Authors: Okike Benjamin, Garba E. J. D.

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The researcher has developed a new encryption technique known as Merged Irregular Transposition Cipher. In this cipher method of encryption, a message to be encrypted is split into parts and each part encrypted separately. Before the encrypted message is transmitted to the recipient(s), the positions of the split in the encrypted messages could be swapped to ensure more security. This work seeks to develop a model by considering the split number, S and the average number of characters per split, L as the message under consideration is split from 2 through 10. Again, after developing the model, the error level in the model would be determined.

Keywords: merged irregular transposition, error level, model estimation, message splitting

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Authors: Josef Slapal

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Digital images are approximations of real ones and, therefore, to be able to study them, we need the digital plane Z2 to be equipped with a convenient structure that behaves analogously to the Euclidean topology on the real plane. In particular, it is required that such a structure allows for a digital analogue of the Jordan curve theorem. We introduce certain adjacency graphs on the digital plane and prove digital Jordan curves for them thus showing that the graphs provide convenient structures on Z2 for the study and processing of digital images. Further convenient structures including the wellknown Khalimsky and Marcus-Wyse adjacency graphs may be obtained as quotients of the graphs introduced. Since digital Jordan curves represent borders of objects in digital images, the adjacency graphs discussed may be used as background structures on the digital plane for solving the problems of digital image processing that are closely related to borders like border detection, contour filling, pattern recognition, thinning, etc.

Keywords: digital plane, adjacency graph, Jordan curve, quotient adjacency

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Saieed Akbari, Yousef Bagheri, Amir Hossein Ghodrati, Sima Saadat Akhtar

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Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.

Keywords: eigenvalues, energy, line graphs, matching number

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: D. K. Soni

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A study of engineering properties of stones, i.e. compressive strength, tensile strength, modulus of elasticity, density, hardness were carried out to explore the possibility of optimum utilization of stone. The laboratory test results on equally dimensioned discs of the stone show a considerable variation in computed split tensile strength with varied rates of deformation. Hence, the effect of strain rate on the tensile strength of a sand stone and lime stone under wet and dry conditions has been studied experimentally using the split tensile strength test technique. It has been observed that the tensile strength of these stone is very much dependent on the rate of deformation particularly in a dry state. On saturation the value of split tensile strength reduced considerably depending upon the structure of rock and amount of water absorption.

Keywords: sedimentary rocks, split tensile test, deformation rate, saturation rate, sand stone, lime stone

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Authors: Bin Sheng, Changhong Lu

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Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

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Authors: Hsiao-Wen Wang

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The split-share structure reform in China represents one of the most significant milestones in the evolution of the capital market. With the goal of converting non-tradable shares into tradable shares, the reform laid the foundation and supported the development of full-scale privatization. This study explores China’s split-share structure reform and its impact on statutory audit fees. This study finds that auditors earn a significant statutory audit fee premium after the split-share structure reform. The Big 4 auditors who provide better audit quality receive higher statutory audit fee premium than non-Big 4 auditors after the share reform, which is attributable to their brand reputation, rather than the relative market dominance.

Keywords: chinese split-share structure reform, statutory audit fees, big-4 auditors, corporate governance

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Authors: Ning Xue, Srinivas Merugu, Ignacio Delgado Martinez, Tao Sun, John Tsang, Shih-Cheng Yen

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We have developed a polyimide based neural interface electrode to record nerve signals from the sciatic nerve of a rat. The neural interface electrode has a split-ring shape, with four protruding gold electrodes for recording, and two reference gold electrodes around the split-ring. The split-ring electrode can be opened up to encircle the sciatic nerve. The four electrodes can be bent to sit on top of the nerve and hold the device in position, while the split-ring frame remains flat. In comparison, while traditional cuff electrodes can only fit certain sizes of the nerve, the developed device can fit a variety of rat sciatic nerve dimensions from 0.6 mm to 1.0 mm, and adapt to the chronic changes in the nerve as the electrode tips are bendable. The electrochemical impedance spectroscopy measurement was conducted. The gold electrode impedance is on the order of 10 kΩ, showing excellent charge injection capacity to record neural signals.

Keywords: impedance, neural interface, split-ring electrode, neural signal recording

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Authors: Nileshkumar Vishnav, Aditya Tatu

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A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

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Authors: Jia-Shiun Chen, Hsiu-Ying Hwang

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Hybrid electric vehicles can reduce pollution and improve fuel economy. Power-split hybrid electric vehicles (HEVs) provide two power paths between the internal combustion engine (ICE) and energy storage system (ESS) through the gears of an electrically variable transmission (EVT). EVT allows ICE to operate independently from vehicle speed all the time. Therefore, the ICE can operate in the efficient region of its characteristic brake specific fuel consumption (BSFC) map. The two-mode powertrain can operate in input-split or compound-split EVT modes and in four different fixed gear configurations. Power-split architecture is advantageous because it combines conventional series and parallel power paths. This research focuses on input-split and compound-split modes in the two-mode power-split powertrain. Fuzzy Logic Control (FLC) for an internal combustion engine (ICE) and PI control for electric machines (EMs) are derived for the urban driving cycle simulation. These control algorithms reduce vehicle fuel consumption and improve ICE efficiency while maintaining the state of charge (SOC) of the energy storage system in an efficient range.

Keywords: hybrid electric vehicle, fuel economy, two-mode hybrid, fuzzy control

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Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

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The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

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Authors: Soner Nandappa D., Ahmed Mohammed Naji

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In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

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Authors: Justine Cyril E. Nunag, Nestor B. Sabado Jr., Jienne Chester M. Tolosa

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Concrete has high compressive strength but a low-tension strength. The small tensile strength of concrete is regarded as its primary weakness, which is why it is typically reinforced with steel, a material that is resistant to tension. Even with steel, however, cracking can occur. In strengthening concrete, only a few researchers have modified the water to be used in a concrete mix. This study aims to compare the split tensile strength of normal structural concrete to concrete prepared with magnetic water and a quick setting admixture. In this context, magnetic water is defined as tap water that has undergone a magnetic process to become magnetized water. To test the hypothesis that magnetized concrete leads to higher split tensile strength, twenty concrete specimens were made. There were five groups, each with five samples, that were differentiated by the number of cycles (0, 50, 100, and 150). The data from the Universal Testing Machine's split tensile strength were then analyzed using various statistical models and tests to determine the significant effect of magnetized water. The result showed a moderate (+0.579) but still significant degree of correlation. The researchers also discovered that using magnetic water for 50 cycles did not result in a significant increase in the concrete's split tensile strength, which influenced the analysis of variance. These results suggest that a concrete mix containing magnetic water and a quick-setting admixture alters the typical split tensile strength of normal concrete. Magnetic water has a significant impact on concrete tensile strength. The hardness property of magnetic water influenced the split tensile strength of concrete. In addition, a higher number of cycles results in a strong water magnetism. The laboratory test results show that a higher cycle translates to a higher tensile strength.

Keywords: hardness property, magnetic water, quick-setting admixture, split tensile strength, universal testing machine

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Authors: Abdallah Sofiane Berrouk, Dara Satyadileep

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This paper investigates the feasibility of retrofitting a middle-east based commercial amine sweetening unit with a split-flow scheme which involves withdrawing a portion of partially stripped semi-lean solvent from the stripping column and re-injecting it in the absorption column to reduce the overall energy consumption of the unit. This method is comprehensively explored by performing parametric analysis of the split fraction of the semi-lean solvent using a kinetics based process simulator ProMax V 3.2. Re-boiler duty, condenser duty, solvent cooling and pumping loads are analysed as functions of a split fraction of the semi-lean solvent from the stripper. It is shown that the proposed method significantly reduces the overall energy consumption of the unit resulting in an annual savings of 325,000 USD. The thorough economic analysis is performed using Aspen Economic Evaluation V 8.4 to reveal that the retrofit scheme pays back the capital cost in less than eight years and is highly recommended for any commercial plant having suitable provisions for solvent inlet/withdrawal on the columns.

Keywords: split flow, Amine, gas processing, optimization

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Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

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Authors: Analen Malnegro, Gina Malacas

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Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.

Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number

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Authors: Hanan Al-Khalaifah, Afaf Al-Nasser

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The egg shell quality and oviposition in laying hens are influenced by a range of factors including strain of birds, age, nutrition, water quality, general stress, heat stress, disease, and lighting program inside houses. A layer experiment was conducted to investigate the effect of split-phase lighting program on egg production efficiency. Four different feeds and average phosphorus (av. P) levels were tested. Diet A was a ration with an av. P level of 0.471%; Diet B was a ration with an av. P level of 0.510%; Diet C contained an av. P level of 0.293%; and Diet D contained an av. P level of 0.327%. The split-phase lighting program tested was one that inserted a 7-hour dark period from 9 am to 4 pm to reduce the heat produced by the feeding increment and physical activity of the hens. Diet B produced significantly more eggs than Diet C, or Diet D. Diet A was not significantly different from any of the other diets. Diet B also had the best feed efficiency with the other three diets in the same order and significance as for egg production. Diet D produced eggshells significantly thicker than either Diet A, or Diet B. Diet C produced thicker eggshells than Diet B, whose shells were significantly thinner than the other three diets. There were no differences in egg size. From these data, it is apparent that the minimal av. P level for the Lohmann strain of layer in Kuwait is above 0.327%. There was no difference in egg production or eggshell thickness between the split-phase light treatment and the standard light program. There was no difference in oviposition frequency. The split-phase light used 3.66% less feed, however, which was significant. The standard light produced eggs that were significantly heavier (66.30g vs. 65.73g). These results indicate that considerable savings in feed costs could be attained by using split-phase lighting, especially when cooling is not very efficient.

Keywords: egg, laying, nutrition, oviposition

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Authors: Ahmed Mohamed El-Shamy, Akram Abbas El-Awady, Mahmoud Taha Eldestawy

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Background: The present study was to evaluate clinically and radiographically the combined effect of split crest technique by ultrasonic bone surgery and platelet concentrates in implant site development. Methods: Forty patients with narrow ridge were participated in this study. Patients were assigned randomly into one of the following four groups according to treatment: Group 1: Patients received split-crest technique by ultrasonic bone surgery with implant placement. Group 2: Patients received split-crest technique by ultrasonic bone surgery with implant placement and PRF. Group 3: Patients received split-crest technique by ultrasonic bone surgery with implant placement and PRP. Group 4: Patients received split-crest technique by ultrasonic bone surgery with implant placement and collagen membrane. Modified plaque index, modified sulcus bleeding index, and implant stability were recorded as a baseline and measured again at 3 and 6 months. CBCT scans were taken immediately after surgery completion and at 9 months to evaluate bone density at the bone-implant interface. Results after 6 months; collagen group showed statistically significantly lower mean modified bleeding index than the other groups. After 3 months, the PRF group showed statistically significantly higher mean implant stability with ostell ISQ units' than the other groups. After 6 months, the PRF group showed statistically significantly higher mean implant stability with ostell ISQ units' than the other groups. After 6 months, the PRF group showed statistically significantly higher mean bone density than the collagen group. Conclusion: Ultrasonic bone surgery in split-crest technique can be a successful option for increasing implant stability values throughout the healing period. The use of a combined technique of ultrasonic bone surgery with PRF and simultaneous implant placement potentially improves osseointegration (bone density). PRF membranes represent advanced technology for the stimulation and acceleration of bone regeneration.

Keywords: dental implants, split-crest, PRF, PRP

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