Fixing number of co-noraml product of graphs

An automorphism of a graph $G$ is a bijective mapping from the vertex set of $G$ to itself which preserves the adjacency and the non-adjacency relations of the vertices of $G$. A fixing set $F$ of a graph $G$ is a set of those vertices of $G$ which when assigned distinct labels removes all the automorphisms of $G$, except the trivial one. The fixing number of a graph $G$, denoted by $fix(G)$, is the smallest cardinality of a fixing set of $G$. The co-normal product $G_1\ast G_2$ of two graphs $G_1$ and $G_2$, is a graph having the vertex set $V(G_1)\times V(G_2)$ and two distinct vertices $(g_1, g_2), (\acute{g_1}, \acute{g_2})$ are adjacent if $g_1$ is adjacent to $\acute{g_1}$ in $G_1$ or $g_2$ is adjacent to $\acute{g_2}$ in $G_2$. We define a general co-normal product of $k\geq 2$ graphs which is a natural generalization of the co-normal product of two graphs. In this paper, we discuss automorphisms of the co-normal product of graphs using the automorphisms of its factors and prove results on the cardinality of the automorphism group of the co-normal product of graphs. We prove that $max\{fix(G_1), fix(G_2)\}\leq fix(G_1\ast G_2)$, for any two graphs $G_1$ and $G_2$. We also compute the fixing number of the co-normal product of some families of graphs.Comment: 13 page

A structural VAR (SVAR) approach to cost channel of monetary policy

The study aims at investigating, whether or not the cost channel of monetary policy is effective in Pakistan. The cost channel is one of the theoretical justifications of Price Puzzle, a phenomenon that has been observed in a number of empirical studies. Using Structural Vector Autoregression (SVAR) and data from different industries of manufacturing sector of Pakistan over the period 2001:M07-2008:M04, we find strong evidence in favor of Price Puzzle in major industries. In industries like textile, food and beverages, pharmaceuticals, automobiles, and fertilizers, cost channel dominates the traditional demand channel. Same behavior is observed for aggregate price level in the overall manufacturing sector. The main reason for the result is the dependency of the above mentioned industries on short-term borrowing to finance their operational liquidity.Cost Channel, Price Puzzle, Working Capital, Monetary Policy, Marginal Cost, Structural Vector Autoregression (SVAR)

Transforming Academic Discourse: A Case Study of International Relations as Discipline

The study of social sciences in general and the discipline of International Relations (IR) in particular, always remained the areas of less scholarly significance, because the leading academic circles remained less-inclined towards the non-western production of knowledge in the international system. The main discussions of IR generally revolve around the western discourse and approaches to knowledge. The end of the decades-long Cold War and the elimination of the Soviet Union from the world politics allowed the Western academic circles to influence the production of knowledge in the international system. In this way, the production of knowledge and the promotion of knowledge ignored the non-western academic perspectives. Contrary to conventional academic patterns, there is a need to realize the significance of non-western literature in academics while updating the conventional academic patterns. In this scenario, this paper attempts to address the questions of the production of knowledge and promotion of knowledge on the basis of relative perspectives. While emphasizing the non-western or non-American approaches to knowledge, the central theme of the paper endeavors to highlight the importance of the non-western way of looking at world politics

At the Crossroads: Exploring the Relationship Between Financial Decisions and Firm Performance of Distressed Firms in the Pakistan Stock Exchange

The primary aim of this study is to assess the influence of financial decisions on the financial performance of distressed firms in Pakistan. Specifically, the research delves into three pivotal financial decisions: dividends, capital structure, and investment choices. Utilising balance sheet analyses published by the State Bank of Pakistan, relevant data were gathered for companies listed on the Pakistan Stock Exchange. The sample for this investigation comprises 185 non-financial firms listed on the PSX over the past eight years (2010-2017), utilising panel data. Regression analysis using the Ordinary Least Squares (OLS) technique was employed to examine the relationships. The results reveal that the dividend policy significantly and positively impacts return on assets, while its effect on return on equity is found to be insignificant. The study also explores the impact of capital structure on the performance of distressed firms, indicating an insignificant and negative effect on return on assets. Additionally, a highly significant positive relationship is identified between taxes and both returns on assets. Concerning return on equity, a negative and highly significant association is observed between long-term debt and ROE. Furthermore, the investigation examines the effects of over- and under-investment on firm performance in distressed firms. The findings suggest that over-investment has a significant and positive impact on return, while under-investment demonstrates a significant and positive effect on return on assets and an insignificant positive impact on return on equity. This study contributes to the understanding of the impact of over and under-investment on firm performance, an aspect not previously explored in distressed firms

Successful treatment of benign lesions by bis 3- azophenyl-4-hydroxy-6-methyl-pyran-2-one cobalt (II) in albino rats

The study of the effect of bis 3-azophenyl-4-hydroxy-6-methyl-pyran-2-one cobalt (II) as chemotherapeutic agent was undertaken with the intention of studying the effects in 7,12-dimethylbenz[a] anthracene (DMBA) and tetradecanoyl phorbol-13-acetate (TPA) induced chemical carcinogenesis on skin of 5 - 7 weeks old healthy albino rats. The animals were divided into 5 groups (A, B, C, D and E) of twenty each. The rats were treated with carcinogens for 15 weeks and then the curative effect of bis 3-azophenyl-4-hydroxy- 6-methyl-pyran-2-one cobalt (II) was observe. The bis 3-azophenyl-4-hydroxy-6-methyl-pyran-2-one cobalt (II) prevents malignant conversion of  chemically induced benign tumors and did not kill cancer cells but change them to normal cells. It was concluded that if the complex is given in the pre-malignant phase of tumor development, it decreases the risk of malignant transformation.Key words: 7,12-Dimethylbenz[a] anthracene (DMBA), tetradecanoyl phorbol-13-acetate (TPA), complex {bis- 3-azophenyl-4-hydroxy-6-methyl-pyran-2-one cobalt (II)}, skin cancer

Synthesis, characterization and antimicrobial potential of transition metal complexes of triacetic lactone

Seven novel and biological active transition metal complexes were prepared using 3-nitro- 4-hydroxy -6-methyl-pyran-2-one derivative of triacetic lactone as ligand. These complexes were characterized by elemental analysis, magnetic susceptibility measurement, UV/Vis, FTIR and NMR spectroscopy. These data showed that solid complexes of Ni (II), Co (II), Mn (II), Zn (II) and Fe (II) indicated octahedral geometries while Cu (II) complex was assigned square planar geometry. The antimicrobial activities ofall above mentioned complexes along with ligand were tested against eleven different bacterial strains and ten fungal strains using agar well diffusion assay. Cu (II) complex showed highest inhibition zone against Shigella dysentriae (22.3 mm), greater than standard drug, while the Zn (II) complex showed maximum antifungal activity against Trichophyton simii (18.7 mm). The antimicrobial activities indicated that metal complexes showed enhanced activity as compared to the free ligand

Impact of Online Trade and Covid-19 on Consumer Behaviour in Covid-19: Evidence from Bank Employees

This research documented the influence of Covid-19 and Online Trade on consumer behaviour in Pakistan. COVID-19 significantly impacts communal health and creates rapid variations in lifestyle, social isolation, and household segregation, with societal and economic effects. This specifies that the country's economic growth in the country has declined. Data is collected through a questionnaire using Google forms from bank employees in Pakistan. SPSS is employed to analyse the data. Results showed a significant and positive relation between online trade and consumer behaviour. It is also revealed that Covid-19 has a negative but significant impact on consumer behaviour. The outcome displays that China is a major producer, and substantial industrial numbers are closed

Competitiveness and Comparative Advantage of Pakistan in Leather and Leather Products Trade: Analysis and Trends

Livestock sector is considered the second key sector of agriculture through its share of more than half to value added and 11.8% to GDP and main source of raw material for leather industry of the country. This local availability of raw materials and low wage cost gives the country a competitive edge in the world market. This study is an effort to examine Pakistan's competitiveness of leather and leather products with a set of Revealed Comparative Advantage (RCA) and Revealed Competitive Advantage index with respect to international trade. The study has utilized Balassa index, Vollrath index and Revealed Symmetric Comparative Advantage index for empirical analysis in Pakistan during the time span from 2003 to 2014. The findings of the study illustrate that Pakistan has a high degree of comparative advantage in this sector during period under analysis which indicates the potential of leather sector exports for foreign exchange earnings. The results of the study also show that the position of Leather sector lies in the “Competitive position product group” and “Threatened product group”. There is need to strengthen comparative and competitive advantage in Leather sector by policy support and facilitating role by all stakeholders to attain the growth in livestock and agriculture sector and improve the income of related stakeholders

n point dct vlsi architecture for emerging hevc standard

This work presents a flexible VLSI architecture to compute the -point DCT. Since HEVC supports different block sizes for the computation of the DCT, that is, up to , the design of a flexible architecture to support them helps reducing the area overhead of hardware implementations. The hardware proposed in this work is partially folded to save area and to get speed for large video sequences sizes. The proposed architecture relies on the decomposition of the DCT matrices into sparse submatrices in order to reduce the multiplications. Finally, multiplications are completely eliminated using the lifting scheme. The proposed architecture sustains real-time processing of 1080P HD video codec running at 150 MHz

LIQUIDITY RISK VS. UNDERINVESTMENT PROBLEM : AN EMPIRICAL STUDY OF THE TEXTILE SECTOR OF PAKISTAN

This research study tests the underinvestment hypothesis andthe liquidity risk hypothesis in the textile sector of Pakistan. A paneldata set of 105 textile companies has been employed over eight yearsextending from 2004-2011. Using 2-Stage Least Square Estimationprocedure (2SLS) and the Generalized Method of Moments (GMM),the empirical findings reveal that textile firms in Pakistan use highlevel of long term debt to shrink the liquidity risk which allows thefirms to use more debt. Moreover growing firms use less leverage thanthe non growing firms when exposed to high growth opportunities.The growth opportunities exhibited a negative relationship with debtmaturity but no significant economic relationship with leverage. Inthe textile sector of Pakistan leverage and short term debt maturitystructure tends to complement each other to hedge the firms againstthe liquidity risk