scholarly journals Some Bicyclic Graphs Having 2 as Their Laplacian Eigenvalues

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1233
Author(s):  
Masoumeh Farkhondeh ◽  
Mohammad Habibi ◽  
Doost Ali Mojdeh ◽  
Yongsheng Rao
Keyword(s):  
Adjacency Matrix ◽  
Perfect Matching ◽  
Laplacian Spectrum ◽  
Laplacian Eigenvalue ◽  
Laplacian Eigenvalues ◽  
Bicyclic Graph ◽  
The Difference ◽  
Vertex Degrees ◽  
Bicyclic Graphs ◽  
The One

If G is a graph, its Laplacian is the difference between the diagonal matrix of its vertex degrees and its adjacency matrix. A one-edge connection of two graphs G 1 and G 2 is a graph G = G 1 ⊙ u v G 2 with V ( G ) = V ( G 1 ) ∪ V ( G 2 ) and E ( G ) = E ( G 1 ) ∪ E ( G 2 ) ∪ { e = u v } where u ∈ V ( G 1 ) and v ∈ V ( G 2 ) . In this paper, we study some structural conditions ensuring the presence of 2 in the Laplacian spectrum of bicyclic graphs of type G 1 ⊙ u v G 2 . We also provide a condition under which a bicyclic graph with a perfect matching has a Laplacian eigenvalue 2. Moreover, we characterize the broken sun graphs and the one-edge connection of two broken sun graphs by their Laplacian eigenvalue 2.

scholarly journals Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muhammad Rizwan ◽  
Akhlaq Ahmad Bhatti ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah
Keyword(s):  
Connected Graph ◽  
Perfect Matching ◽  
Matching Number ◽  
Bicyclic Graph ◽  
Bicyclic Graphs ◽  
Extremal Values

A connected graph G V , E in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set such that the number of vertices is two times its matching number. In this paper, we investigated maximum and minimum values of variable sum exdeg index, SEI a for bicyclic graphs with perfect matching for k ≥ 5 and a > 1 .

scholarly journals Effects on the distance Laplacian spectrum of graphs with clusters by adding edges

2019 ◽  
Vol 35 ◽  
pp. 511-523
Author(s):  
Roberto Díaz ◽  
Oscar Rojo
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
Laplacian Spectrum ◽  
Laplacian Eigenvalue ◽  
Laplacian Eigenvalues ◽  
The Matrix ◽  
Spectrum Of Graphs

All graphs considered are simple and undirected. A cluster in a graph is a pair of vertex subsets (C, S), where C is a maximal set of cardinality |C| ≥ 2 of independent vertices sharing the same set S of |S| neighbors. Let G be a connected graph on n vertices with a cluster (C, S) and H be a graph of order |C|. Let G(H) be the connected graph obtained from G and H when the edges of H are added to the edges of G by identifying the vertices of H with the vertices in C. It is proved that G and G(H) have in common n −|C| + 1 distance Laplacian eigenvalues, and the matrix having these common eigenvalues is given, if H is the complete graph on |C| vertices then ∂ −|C| + 2 is a distance Laplacian eigenvalue of G(H) with multiplicity|C| − 1, where ∂ is the transmission in G of the vertices in C. Furthermore, it is shown that if G is a graph of diameter at least 3, then the distance Laplacian spectral radii of G and G(H) are equal, and if G is a graph of diameter 2, then conditions for the equality of these spectral radii are established. Finally, the results are extended to graphs with two or more disjoint clusters.

scholarly journals The least Laplacian eigenvalue of the unbalanced unicyclic signed graphs with $k$ pendant vertices

2020 ◽  
Vol 36 (36) ◽  
pp. 390-399
Author(s):  
Qiao Guo ◽  
Yaoping Hou ◽  
Deqiong Li
Keyword(s):  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
Signed Graph ◽  
Signed Graphs ◽  
Laplacian Eigenvalue ◽  
Unicyclic Graphs ◽  
Underlying Graph ◽  
Vertex Degrees

Let $\Gamma=(G,\sigma)$ be a signed graph and $L(\Gamma)=D(G)-A(\Gamma)$ be the Laplacian matrix of $\Gamma$, where $D(G)$ is the diagonal matrix of vertex degrees of the underlying graph $G$ and $A(\Gamma)$ is the adjacency matrix of $\Gamma$. It is well-known that the least Laplacian eigenvalue $\lambda_n$ is positive if and only if $\Gamma$ is unbalanced. In this paper, the unique signed graph (up to switching equivalence) which minimizes the least Laplacian eigenvalue among unbalanced connected signed unicyclic graphs with $n$ vertices and $k$ pendant vertices is characterized.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

The Demand For Money in Pakistan: Reply (Notes and Comments)

1975 ◽  
Vol 14 (3) ◽  
pp. 370-375
Author(s):  
M. A. Akhtar
Keyword(s):  
Interest Rates ◽  
Money Demand ◽  
Strong Support ◽  
Physical Capital ◽  
Careful Examination ◽  
Demand For Money ◽  
Weak Support ◽  
Complementarity Hypothesis ◽  
The Difference ◽  
The One

I am grateful to Abe, Fry, Min, Vongvipanond, and Yu (hereafter re¬ferred to as AFMVY) [1] for obliging me to reconsider my article [2] on the demand for money in Pakistan. Upon careful examination, I find that the AFMVY results are, in parts, misleading and that, on the whole, they add very little to those provided in my study. Nevertheless, the present exercise as well as the one by AFMVY is useful in that it furnishes us with an opportunity to view some of the fundamental problems involved in an empi¬rical analysis of the demand for money function in Pakistan. Based on their elaborate critique, AFMVY reformulate the two hypo¬theses—the substitution hypothesis and the complementarity hypothesis— underlying my study and provide us with some alternative estimates of the demand for money in Pakistan. Briefly their results, like those in my study, indicate that income and interest rates are important in deter¬mining the demand for money. However, unlike my results, they also suggest that the price variable is a highly significant determinant of the money demand function. Furthermore, while I found only a weak support for the complementarity between money demand and physical capital, the results obtained by AFMVY appear to yield a strong support for that rela¬tionship.1 The difference in results is only a natural consequence of alter¬native specifications of the theory and, therefore, I propose to devote most of this reply to the criticisms raised by AFMVY and the resulting reformulation of the two mypotheses.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

Development and Validation of Spectrophotometric and Liquid Chromatographic Methods for Estimation of Tigecycline in Injections

2020 ◽  
Vol 13 (5) ◽  
pp. 5148-5154
Author(s):  
Sagar Suman Panda ◽  
Ravi Kumar B.V.V.
Keyword(s):  
Area Under The Curve ◽  
Reversed Phase ◽  
Equal Concentration ◽  
Pharmaceutical Dosage Form ◽  
Liquid Chromatographic Method ◽  
Array Detection ◽  
The Difference ◽  
The One ◽  
Development And Validation ◽  
Liquid Chromatographic

Three new analytical methods were optimized and validated for the estimation of tigecycline (TGN) in its injection formulation. A difference UV spectroscopic, an area under the curve (AUC), and an ultrafast liquid chromatographic (UFLC) method were optimized for this purpose. The difference spectrophotometric method relied on the measurement of amplitude when equal concentration solutions of TGN in HCl are scanned against TGN in NaOH as reference. The measurements were done at 340 nm (maxima) and 410nm (minima). Further, the AUC under both the maxima and minima were measured at 335-345nm and 405-415nm, respectively. The liquid chromatographic method utilized a reversed-phase column (150mm×4.6mm, 5µm) with a mobile phase of methanol: 0.01M KH2PO4 buffer pH 3.5 (using orthophosphoric acid) in the ratio 80:20 %, v/v. The flow rate was 1.0ml/min, and diode array detection was done at 349nm. TGN eluted at 1.656min. All the methods were validated for linearity, precision, accuracy, stability, and robustness. The developed methods produced validation results within the satisfactory limits of ICH guidance. Further, these methods were applied to estimate the amount of TGN present in commercial lyophilized injection formulations, and the results were compared using the One-Way ANOVA test. Overall, the methods are rapid, simple, and reliable for routine quality control of TGN in the bulk and pharmaceutical dosage form. 

Managing the Era of Multi-Cultural Leadership

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Rahul ◽  
R. Ganesan
Keyword(s):  
Work Environment ◽  
Leadership Style ◽  
Work Experience ◽  
Cross Culture ◽  
Cultural Leadership ◽  
Team Members ◽  
Diverse Workforce ◽  
The Difference ◽  
The One ◽  
Global Arena

Leaders in the global arena are the one who face the challenges never seen before, while coordinating work and managing relationship between team members coming from varied ethnic groups. Globalization has undoubtedly opened up endless growth opportunities for both, businesses and individuals, by collaborating with each other, but with certain inherent challenges. These challenges are the difference in the cultural background of the team members, which gets predominantly reflected in their behavior at workplace too. The cultural differences exist primarily due to differences in shared values, which form the basis for difference in perception and practices of decision making by an individual (Hofstede, 1980). Juana Bordas has rightly described that any business that fails to adapt their leadership style aligning with multi-cultural approach will find it difficult to thrive in a more colorful world. Leadership style has witnessed various facets of changing work environment that has demanded from leaders to modify their approach to adapt along and be effective and survive in the ever-changing environment of business (Bordas,2007).A cross-culture leader plays a significant role in knitting the diverse workforce into an efficient team; which requires a leader to very well understand the various dimensions of culture. This understanding of the leader enables him to learn about blending of leadership styles to address the challenges of such work environment. This paper is an extended work on 'Leadership in Cross-Cultural Environment – A Comparison of Asian and Non-Asian Managers' (Rahul and Ganesan, 2015). The extended research study has identified that enhanced work experience of cross-culture leaders enables them in effective team management, than the rise in designation, as it results in creation of hierarchical distance between the leaders and subordinates.

Defending the Difference

2017 ◽  
Keyword(s):  
Social Sciences ◽  
Natural Sciences ◽  
Point Of View ◽  
True Nature ◽  
Natural Entities ◽  
The Social ◽  
The World ◽  
Methodological Difference ◽  
The Difference ◽  
The One

Dreyfus argues that there is a basic methodological difference between the natural sciences and the social sciences, a difference that derives from the different goals and practices of each. He goes on to argue that being a realist about natural entities is compatible with pluralism or, as he calls it, “plural realism.” If intelligibility is always grounded in our practices, Dreyfus points out, then there is no point of view from which one can ask about or provide an answer to the one true nature of ultimate reality. But that is consistent with believing that the natural sciences can still reveal the way the world is independent of our theories and practices.

scholarly journals Major Elements to Consider in Developing Ammonia Emission Factor at Municipal Solid Waste (MSW) Incinerators

2021 ◽  
Vol 13 (4) ◽  
pp. 2197
Author(s):  
Seongmin Kang ◽  
Joonyoung Roh ◽  
Eui-chan Jeon
Keyword(s):  
Municipal Solid Waste ◽  
Solid Waste ◽  
Emission Factor ◽  
Waste Incineration ◽  
Emission Factors ◽  
Major Elements ◽  
Ammonia Emission ◽  
Nh3 Emission ◽  
The Difference ◽  
The One

NH3 is one of the major substances contributing to the secondary generation of PM2.5; therefore, management is required. In Korea, the management of NH3 is insufficient, and the emission factor used by EPA is the same as the one used when calculating emissions. In particular, waste incineration facilities do not currently calculate NH3 emissions. In the case of combustion facilities, the main ammonia emission source is the De-NOx facility, and, in the case of a power plant with a De-NOx facility, NH3 emission is calculated. Therefore, in the case of a Municipal Solid Waste (MSW) incinerator with the same facility installed, it is necessary to calculate NH3 emissions. In this study, the necessity of developing NH3 emission factors for an MSW incinerator and calculating emission was analyzed. In addition, elements to be considered when developing emission factors were analyzed. The study found that the NH3 emission factors for each MSW incinerator technology were calculated as Stoker 0.010 NH3 kg/ton and Fluidized Beds 0.004 NH3 kg/ton, which was greater than the NH3 emission factor 0.003 NH3 kg/ton for the MSW incinerator presented in EMEP/EEA (2016). As a result, it was able to identify the need for the development of NH3 emission factors in MSW incinerators in Korea. In addition, the statistical analysis of the difference between the incineration technology of MSW and the NH3 emission factor by the De-NOx facility showed a difference in terms of both incineration technology and De-NOx facilities, indicating that they should be considered together when developing the emission factor. In addition to MSW, it is believed that it will be necessary to review the development of emission factors for waste at workplaces and incineration facilities of sewage sludge.

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