Symmetric Entry Research Articles

Characterizing signed mixed graphs with small eigenvalues

A mixed graph MG is obtained from a simple graph G by orienting an edge subset of G. A signed mixed graph is a mixed graph with arcs and edges signed + or −. The unit Eisenstein matrix (E-matrix for short) of a signed mixed graph was recently introduced by Wissing and van Dam [32]. This novel matrix is indexed by the vertices of the signed mixed graph, and the entry corresponding to a positive arc from u to v is equal to ω=1+i32 (and its symmetric entry is ω‾=1−i32); the entry corresponding to a negative arc is equal to −ω (and its symmetric entry is −ω‾); the entry corresponding to a positive edge is equal to 1; the entry corresponding to a negative edge is equal to −1; and 0 otherwise. In this paper, we study the spectral properties of this E-matrix. We characterize all the signed mixed graphs whose eigenvalues are contained in (−α,α) for α∈{2,3,2}.

Mixed graphs whose Hermitian adjacency matrices of the second kind have the smallest eigenvalue greater than [formula omitted

Mixed graphs unify simple graphs and oriented graphs naturally. The Hermitian adjacency matrix of a mixed graph for the second kind (N-matrix for short) was recently introduced by Mohar [13]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the principal sixth root of unity ω=1+i32 (and its symmetric entry is ω‾=1−i32); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. In this paper, we completely characterize the connected mixed graphs whose N-matrices have the smallest eigenvalue greater than −32. It may be considered as the continuance of the work of J.H. Smith [18] who considered the classical problem of characterizing the graphs whose eigenvalues lie in a given interval.

Resale in second‐price auctions with private entry

AbstractThis paper investigates the effects of resale on bidders' entry decisions, social welfare, and seller's expected revenue in a second‐price auction with two‐dimensional private information on values and participation costs. We establish the existence of symmetric entry equilibrium and identify sufficient conditions under which the equilibrium is unique. We show that when resale is allowed, the low‐cost bidders become more aggressive on entry, while the high‐cost bidders are less likely to enter. Furthermore, our analysis also suggests resale allowance can increase the social welfare under a sufficient condition, which depends on the magnitude of bargaining power, and its effect on expected revenue is ambiguous.

The k-generalized Hermitian adjacency matrices for mixed graphs

This article gives some fundamental introduction to spectra of mixed graphs via its k-generalized Hermitian adjacency matrix. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the kth root of unity e2πik (and its symmetric entry is e−2πik); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. For all positive integers k, the non-zero entries of the above matrix are chosen from the gain set {1,e2πik,e−2πik}, which is not closed under multiplication when k⩾4. In this paper, for all positive integers k, we extract all the mixed graphs whose k-generalized Hermitian adjacency rank (Hk-rank for short) is 3, which partially answers a question proposed by Wissing and van Dam [34]. Furthermore, we study the spectral determination of mixed graphs with Hk-rank 2 and 3, respectively.

Hermitian adjacency matrix of the second kind for mixed graphs

This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind (N-matrix for short) introduced by Mohar [25]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity ω=1+i32 (and its symmetric entry is ω¯=1−i32); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: equivalent conditions for a mixed graph that shares the same spectrum of its N-matrix with its underlying graph are given. A sharp upper bound on the spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called two-way and three-way switchings are discussed–they give rise to some cospectral mixed graphs. We extract all the mixed graphs whose rank of its N-matrix is 2 (resp. 3). Furthermore, we show that if MG is a connected mixed graph with rank 2, then MG is switching equivalent to each connected mixed graph to which it is cospectral. However, this does not hold for some connected mixed graphs with rank 3. We identify all mixed graphs whose eigenvalues of its N-matrix lie in the range (−α,α) for α∈{2,3,2}.

Competing first-price and second-price auctions

This paper theoretically investigates which auctions are selected by competing sellers when they can choose between first-price auctions and second-price auctions, and when homogeneously risk averse bidders endogenously enter one of the auctions. In order to study this, we first consider bidders’ entry decisions between exogenously given auctions. We find that there exists a symmetric entry equilibrium that is unique and is characterized by a mixed strategy, which depends on whether bidders exhibit constant, decreasing or increasing absolute risk aversion. In a next step, we endogenize the sellers’ choice of auctions. We show that competing sellers have a dominant strategy to select first-price auctions if bidders exhibit nondecreasing absolute risk aversion. If bidders exhibit decreasing absolute risk aversion, other equilibria may exist in which sellers select second-price auctions as well. For instance, we demonstrate that sellers may select second-price auctions if the distribution of private values is sufficiently skewed.

Eigenvectors of random matrices of symmetric entry distributions

Eigenvectors of random matrices of symmetric entry distributions

Combination of the Methods of symmetrical components and Double Entry to Increase the Reliability of Digital Differential Relay Protection

The method of symmetrical components is one of the main methods used to calculate asymmetric modes in electric power systems. To increase the reliability of digital differential relay protection in case of asymmetric faults, a combination of symmetric components and double entry methods is proposed. It is supposed to compile balance equations, to apply the theory of graphs and matrices, and the estimation of reliability indicators is carried out on the basis of the method of Markov chains. The obtained results allow to make a conclusion about the prospects of implementing a differential protection using the method of double entry and symmetrical components in the electrical networks.

Hermitian Adjacency Matrix of Digraphs and Mixed Graphs

AbstractThe article gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from x to y is equal to the complex unity i (and its symmetric entry is ) if the reverse arc is not present. We also allow arcs in both directions and unoriented edges, in which case we use 1 as the entry. This allows to use the definition also for mixed graphs. This matrix has many nice properties; it has real eigenvalues and the interlacing theorem holds for a digraph and its induced subdigraphs. Besides covering the basic properties, we discuss many differences from the properties of eigenvalues of undirected graphs and develop basic theory. The main novel results include the following. Several surprising facts are discovered about the spectral radius; some consequences of the interlacing property are obtained; operations that preserve the spectrum are discussed—they give rise to a large number of cospectral digraphs; for every , all digraphs whose spectrum is contained in the interval are determined.

Surface Roughness Effect on the Performance of 3-lobe Symmetric Hole Entry Hybrid Journal Bearings

The present paper, evaluates the effect of surface roughness on the performance characteristics of capillary compensated 3-lobe symmetric hole entry hybrid journal bearing. The effect of surface roughness patterns viz; transverse, isotropic, longitudinal and smooth, on bearing performance is presented for different values of offset factor. A modified form of Reynold’s equation in conjunction with restrictor flow equation is solved by using Galerkin’s technique of FEM. The numerically simulated results of the study indicate that the surface roughness orientation patterns affect the performance of 3-lobe hybrid journal bearing system significantly. Further, it is noticed that the longitudinal roughness pattern provides enhanced value of rotor dynamic coefficient.To have an improved dynamic performance, a judicious selection of offset factor and surface roughness pattern parameter is essential.

Too Much of a Good Thing? Welfare Consequences of Market Transparency

This paper studies welfare consequences of consumer-side market transparency with endogenous entry of firms. Different from most studies, we consider the unique symmetric entry equilibrium, which is in mixed strategies. We identify two effects of market transparency on welfare: a competition effect and a novel market-structure effect. We show, surprisingly, that for almost all demand functions the negative market-structure effect eventually dominates the positive competition effect as the market becomes increasingly transparent. Consumer-side market transparency can therefore be socially excessive even without collusion. The only exception among commonly used demand functions is the set of constant demand functions.

Auctions with entry and resale

We study how resale affects auctions with costly entry in a model where bidders possess two-dimensional private information signals: entry costs and valuations. We establish the existence of symmetric entry equilibrium and identify sufficient conditions under which the equilibrium is unique. Our analysis suggests that the opportunity of resale affects both entry and bidding, and, in particular, it induces motivation for speculative entry and resale hunting abstentions. Our numerical results suggest that while expected entry is higher when resale is allowed, the effects of resale on expected revenue and efficiency are both ambiguous.

Free Trade vs. Autarky in an Asymmetric Cournot World

The paper first demonstrates that in a simple asymmetric n-country world with Cournot competition, constant returns and linear demand, free trade can reduce world welfare as well as total output and consumer surplus. We then derive precise conditions for free trade to raise a country’s welfare, consumer surplus, profits etc. and demonstrate how these conditions are linked in a clear order. We also show that free trade always raises the sum of social welfare and consumer surplus in every country. Finally, we show that with symmetric costs or free entry and exit, there are always global gains from free trade.

Some Comparative Statics Of Entry In Markets With Demand Complementarities

This paper develops a two-market Cournot model with complementary demands to investigate comparative statics associated with symmetric and asymmetric entry. Notably, while market prices are decreasing with the number of market rivals, asymmetric entry actually causes prices to rise in the adjacent, complementary market. In addition, the price-decreasing effects of symmetric entry are attenuated with strong cross-price effects.

A Chiral‐Pool‐Based Approach to the Core Structure of (+)‐Hyperforin

AbstractAsymmetric entry to the bicyclic core structure of (+)‐hyperforin is presented. The developed synthetic strategy features a carefully orchestrated stereochemical relay from the single chiral center residing within (–)‐Wieland–Miescher ketone and an intramolecular aldol reaction to cast the [3.3.1] bicyclic scaffold found in a diverse array of polycyclic polyprenylated acylphloroglucinols.

CFD modeling of 2D impact with symmetric entry

The 2D impact phenomenon in calm water, considering symmetric entry with vertical velocity is studied. The analysis was performed by using commercial STAR-CCM+ computational fuid dynamics software. Thee results obtained from the simulations are pressure distribution and force during impact. The study was carried out for typical planning of boat sections. The results are compared with models and data obtained from some authors and they present very good agreement.

Soybean Crush Spread Arbitrage: Trading Strategies and Market Efficiency

This paper revisits the soybean crush spread arbitrage work of Simon (JFM, 1999). Major findings are that contrary to the results reported by Simon, the length of winning and losing trades differ systematically. Winning trades are significantly shorter on average than losing trades. This result leads to trading rules designed to prevent lengthy trades. Secondly, the work by Simon employs symmetric entry and exit limits. That approach assumes that the market overshoots equilibrium. This research studies a wide variety of entry and exit limits and the risk-return relationship between the entry and exit limits.

Free Riding in Noncooperative Entry Deterrence with Differentiated Products

We examine free riding and underinvestment in noncooperative entry deterrence in the Gilbert and Vives (1986) model with differentiated products. Our analysis proves that for products that are differentiated enough, when both entry allowing and entry deterring equilibria coexist, the symmetric entry deterring equilibrium may Pareto dominate the entry equilibrium. Hence, “coordination failure” underinvestment in entry prevention can occur. However, as claimed, the overinvestment result of Gilbert and Vives remains robust to moderate amounts of product differentiation. We also show that coordination failure underinvestment arises in a wide variety of entry deterrence models and does not rely on assumptions regarding strategic substitutability or complementarity of precommitments.

Five syndromes (malformation complexes) of pulmonary symmetry, congenital heart disease, and multiple spleens.

The most common multiple anomaly complex with pulmonary isomerism and congenital heart disease is the Ivemark asplenia syndrome.’ Regular features of this disorder include: pulmonary isomerism of right lung type, with three lobar bronchi in each lung; congenital heart disease, typically single ventricle and functionally common atria, with the great arteries in the position of transposition, plus pulmonic stenosis or atresia; anomalous pulmonary venous connection and anomalous systemic venous patterns; abnormal visceral situs, with intestinal malrotation and symmetric liver; absence of the spleen; two-thirds predominance of male sex and right aortic arch.2 The proposal that the Ivemark syndrome is the result of “bilateral right-~idedness”~ is supported by: 1. Pulmonary isomerism of right lung type 2. Absence of the spleen, which is the only major viscus that develops entirely on the left side of the body 3. Symmetric entry of the right and left superior venae cavae into the right and left atrial chambers, both of which have the anatomy of right atria4 4. High frequency of extracardiac pulmonary venous connection.2 (In the sense that both atria are embryologically right atria, into which pulmonary veins do not normally enter, both cardiac and extracardiac venous connections are embryologically anomalous in this disorder.)

Approximate Impact Dispersion Methods for Symmetric Entry Vehicles

Approximate Impact Dispersion Methods for Symmetric Entry Vehicles