Search results for: Connection Existence Period (CEP)

Authors: Zeynep Orman, Sabri Arik

Abstract:

This paper presents a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for Cohen-Grossberg neural networks with multiple time delays. The results establish a relationship between the network parameters of the neural system independently of the delay parameters. The results are also compared with the previously reported results in the literature.

Keywords: Equilibrium and stability analysis, Cohen-Grossberg Neural Networks, Lyapunov Functionals.

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Authors: Yongkun Li, Kaihong Zhao

Abstract:

By using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results.

Keywords: Positive periodic solutions, Lotka-Volterra competition system, coincidence degree, harvesting term.

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Authors: Madhukar Nagare, Pankaj Dutta

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Inventory decisional environment of short life-cycle products is full of uncertainties arising from randomness and fuzziness of input parameters like customer demand requiring modeling under hybrid uncertainty. Prior inventory models incorporating fuzzy demand have unfortunately ignored stochastic variation of demand. This paper determines an unambiguous optimal order quantity from a set of n fuzzy observations in a newsvendor inventory setting in presence of fuzzy random variable demand capturing both fuzzy perception and randomness of customer demand. The stress of this paper is in providing solution procedure that attains optimality in two steps with demand information availability in linguistic phrases leading to fuzziness along with stochastic variation. The first step of solution procedure identifies and prefers one best fuzzy opinion out of all expert opinions and the second step determines optimal order quantity from the selected event that maximizes profit. The model and solution procedure is illustrated with a numerical example.

Keywords: Fuzzy expected value, Fuzzy random demand, Hybrid uncertainty, Optimal order quantity, Single-period inventory

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Authors: Zhengyi Kong, Seung-Eock Kim

Abstract:

Single angle connections, which are bolted to the beam web and the column flange, are studied to investigate their moment-rotation behavior. Elastic–perfectly plastic material behavior is assumed. ABAQUS software is used to analyze the nonlinear behavior of a single angle connection. The identical geometric and material conditions with Lipson’s test are used for verifying finite element models. Since Kishi and Chen’s Power model and Lee and Moon’s Log model are accurate only for a limited range of mechanism, simpler and more accurate hyperbolic function models are proposed.

Keywords: Single-web angle connections, finite element method, moment and rotation, hyperbolic function models.

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Authors: Syed Javed Arif, Mohd Ayyub Khan, Saleem Anwar Khan

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In this paper, a simple method is presented for measurement of power frequency deviations. A phase locked loop (PLL) is used to multiply the signal under test by a factor of 100. The number of pulses in this pulse train signal is counted over a stable known period, using decade driving assemblies (DDAs) and flip-flops. These signals are combined using logic gates and then passed through decade counters to give a unique combination of pulses or levels, which are further encoded. These pulses are equally suitable for both control applications and display units. The experimental circuit developed gives a resolution of 1 Hz within the measurement period of 20 ms. The proposed circuit is also simulated in Verilog Hardware Description Language (VHDL) and implemented using Field Programing Gate Arrays (FPGAs). A Mixed signal Oscilloscope (MSO) is used to observe the results of FPGA implementation. These results are compared with the results of the proposed circuit of discrete components. The proposed system is useful for frequency deviation measurement and control in power systems.

Keywords: Frequency measurement, digital control, phase locked loop, encoding, Verilog HDL.

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Authors: Hilmi Yazici

Abstract:

The more homogenized population taken over by the Republic immediately after the Ottoman was being canalized towards the goal of national identity and the historical and cultural structure of the nation was being readdressed and redefined. Modernization and Westernization history of the new Turkey, which started with Ottoman reforms and took its final form with the Kemalist nation-state, politically resulted in transformation from a multinational empire to a “nation-state” and adopted reaching to the level of Western civilizations as a sociology ideal. This objective of change will be achieved, on the one hand, by finding the Turkish culture which was preserved only by the society and by instilling Western civilization to national culture, on the other hand.  In line with this, it is seen that in musical considerations while Turkish folk music was accepted and adopted as an indispensible part of Turkish identity, Turkish classical music was refused on the ground that it was not a part of Turkish identity. Again in this period, it is seen that with the notion of cultural reform, which is a part of “nation building”, the desire to create a national music to be performed with Western techniques brought along deliberate interventions to folk music.

Keywords: Folk song, Nationalism, National music, nation-state, Turkish music.

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Authors: Benshi Zhu

Abstract:

In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method.

Keywords: Discrete boundary value problems, nonsmoothcritical point theory, positive solutions, semipositone, sub-super solutions method

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Authors: Josiane R. Pires, Marco A. S. González, Bruna L. Brenner, Luciana S. Roos

Abstract:

The concern with sustainability brought the need for optimization of the buildings to reduce consumption of natural resources. Almost 1/3 of energy demanded by Brazilian housings is used to provide thermal solutions. AEC sector may contribute applying bioclimatic strategies on building design. The aim of this research is to investigate the viability of applying some alternative solutions in residential buildings. The research was developed with computational simulation on single family social housing, examining envelope type, absorptance, and insolation. The analysis of the thermal performance applied both Brazilian standard NBR 15575 and degree-hour method, in the scenery of Porto Alegre, a southern Brazilian city. We used BIM modeling through Revit/Autodesk and used Energy Plus to thermal simulation. The payback of the investment was calculated comparing energy savings and building costs, in a period of 50 years. The results shown that with the increment of envelope’s insulation there is thermal comfort improvement and energy economy, with a pay-back period of 24 to 36 years, in some cases.

Keywords: Civil construction, design, thermal performance, energy, economic analysis.

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Authors: Muhammad Naeem, Abdus Salam, Muhammad Ashraf, Muhammad Imran, Mehtab Ahmad, Muhammad Jamshed Khan, Muhammad Mazhar Ayaz, Muzaffar Ali, Arshad Ali, Memoona Qayyum Abir Ishtiaq

Abstract:

The present study was designed to demonstrate the seasonal variations in physico-chemical parameters of fish farm at Govt. Nursery Unit, Muzaffargarh, Department of Fisheries Govt. of Punjab, Pakistan for a period of eight months from January to August 2008. Water samples were collected on fifteen days basis and have been analyzed for estimation of Air temperature, Water temperature, Light penetration, pH, Total dissolved oxygen, Clouds, Carbonates, Bicarbonates, Total carbonates, Total dissolved solids, Chlorides, Calcium and Hardness. Seasonal fluctuations were observed in all the physico-chemical parameters of fish farm. The overall physicochemical parameters of fish pond water remained within the tolerable range throughout the study period.

Keywords: Freshwater, Fish farm, Water quality, Seasonal variation, Chemical factor

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Authors: Sorcha Bennett, Joe Sullivan

Abstract:

Triple-Level Cell (TLC) NAND Flash memory at, and below, 20nm (nanometer) is still largely unexplored by researchers, and with the ever more commonplace existence of Flash in consumer and enterprise applications there is a need for such gaps in knowledge to be filled. At the time of writing, there was little published data or literature on TLC, and more specifically reliability testing, with a further emphasis on both endurance and retention. This paper will give an introduction to NAND Flash memory, followed by an overview of the relevant current research on the reliability of Flash memory, along with the planned future work which will provide results to help characterise the reliability of TLC memory.

Keywords: TLC NAND flash memory, reliability, endurance, retention, trade-off, raw flash, patterns.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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Authors: Hiraku Nunomiya, Takuo Ichiju, Yoshiyuki Higuchi

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In the management of industrial waste, conversion from the use of paper invoices to electronic forms is currently under way in developed countries. Difficulties in such computerization include the lack of synchronization between the actual goods and the corresponding data managed by the server. Consequently, a system which utilizes the incorporation of a QR code in connection with the waste material has been developed. The code is read at each stage, from discharge until disposal, and progress at each stage can be easily reported. This system can be linked with Japanese public digital authentication service of waste, taking advantage of its good points, and can be used to submit reports to the regulatory authorities. Its usefulness was confirmed by a verification test, and put into actual practice.

Keywords: Infectious Waste, Electronic Manifest, Real Time Management, QR code.

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Authors: Zhalmagambetov Yerlanbek, Assymova Dariya, Tashieva Saltanat, and Aliya Bolatkhan

Abstract:

The relevance of the study of everyday life in Almaty and Kyzylorda are associated with the emergence of the modern trends in historiography and socializing areas of government reform. The relevance is due to the fact that in the early twentieth century Kyzylorda and Almaty began to develop as a city and this period has a special place in the life of the state. An interesting aspect of the everyday life of the inhabitants of the new city, which was built in the era of Stalin's Five-Year Plans, can be examined through the eyes of the Soviet people living in a specific environment, reflecting the life of the citizens. The study of industrialization of the Soviet Union and the attention paid to new developments in the first five years of everyday aspects as the impact of the modernization of the 1930s was one of the decisive factors in the lives of residents. Among these factors, we would like to highlight the medical field, which is the basis of all human life, specifically focusing on the state of medicine in Alma-Ata in the first 20-30-years of the twentieth century, and analyze the different aspects of human life, determining the quality of medical care to the population during this period.

Keywords: Alma Ata, capital, epidemic diseases, health care, Kyzylorda, the USSR, Vernyj.

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Authors: J. M. B. Mendonça, M. V. S. Siqueira, A. Soares, M. A. F. Santos

Abstract:

The purpose of this article is to understand the dynamics of the increase in incivility through social relations (gender, race, class, sexual orientation, etc.), which hide inequalities in the form of treatment and opportunities within the organizational sphere. For this, we will examine works that address incivility at work, as well as studies that deviate from the mainstream, bringing more obscure organizational facets to light in connection with a critical approach to this issue. Next, some results of a bibliometric study shall be exposed, to analyze contributions connected to the theme and demonstrate gaps for future research. Then, models that facilitate reflection on the dynamics of violence shall be discussed. Finally, a broader concept of incivility in interpersonal relationships in the workplace shall be exposed considering the multiple approaches discussed.

Keywords: Incivility, inequalities, organization reflections, preventing violence.

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Authors: Lv Yuhua

Abstract:

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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Authors: Andreas L. Savvides

Abstract:

The proposed paper examines strategies whose aim is to counter the all too often sighted process of abandonment that characterizes contemporary cities. The city of Nicosia in Cyprus is used as an indicative case study, whereby several recent projects are presented as capitalizing on traditional cultural assets to revive the downtown. The reuse of existing building stock as museums, performing arts centers and theaters but also as in the form of various housing typologies is geared to strengthen the ranks of local residents and to spur economic growth. Unlike the examples from the 1960s, the architecture of more recent adaptive reuse for urban regeneration seems to be geared in reinforcing a connection to the city where the buildings often reflect the characteristics of their urban context.

Keywords: Public Housing, Building Rehabilitation, Urban Regeneration, Population Integration

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Authors: A.Chetaine, A. Benchrif, H. Amsil, V. Kuznetsov, Y. Shimazu

Abstract:

The evaluation of unit cell neutronic parameters and lifetime for some innovant reactors without on sit-refuling will be held in this work. the behavior of some small and medium reactors without on site refueling with triso and cermet fuel. For the FBNR long life except we propose to change the enrichment of the Cermet MFE to 9%. For the AFPR reactor we can see that the use of the Cermet MFE can extend the life of this reactor but to maintain the same life period for AFPR-SC we most use burnup poison to have the same slope for Kinf (Burnup). PFPWR50 cell behaves almost in same way using both fuels Cermet and TRISO. So we can conclude that PFPWR50 reactor, with CERMET Fuel, is kept among the long cycle reactors and with the new configuration we avoid subcriticality at the beginning of cycle. The evaluation of unit cell neutronic parameters reveals a good agreement with the goal of BWR-PB concept. It is found out that the Triso fuel assembly lifetime can be extended for a reasonably long period without being refueled, approximately up to 48GWd/t burnup. Using coated particles fuels with the Cermet composition can be more extended the fuel assembly life time, approximately 52 GWd/t.

Keywords: Cermet., Trisot, without on site refueling.

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Authors: Mosaad Khadr, Gerd Morgenschweis, Andreas Schlenkhoff

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Drought is one of the most damaging climate-related hazards, it is generally considered as a prolonged absence of precipitation. This normal and recurring climate phenomenon had plagued civilization throughout history because of the negative impacts on economical, environmental and social sectors. Drought characteristics are thus recognized as important factors in water resources planning and management. The purpose of this study is to detect the changes in drought frequency, persistence and severity in the Ruhr river basin. The frequency of drought events was calculated using the Standardized Precipitation Index (SPI). Used data are daily precipitation records from seven meteorological stations covering the period 1961-2007. The main benefit of the application of this index is its versatility, only rainfall data is required to deliver five major dimensions of a drought : duration, intensity, severity, magnitude, and frequency. Furthermore, drought can be calculated in different time steps. In this study SPI was calculated for 1, 3, 6, 9, 12, and 24 months. Several drought events were detected in the covered period, these events contain mild, moderate and severe droughts. Also positive and negative trends in the SPI values were observed.

Keywords: Drought, Germany, Precipitation, Ruhr River, Standardized Precipitation Index (SPI), Trend Test.

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Authors: M. M. Mohammadi Dehnavi, A. De Angelis, M. R. Pecce

Abstract:

This paper deals with the role of studs in structural response for steel-concrete composite beams. A tri-linear slip-shear strength law is assumed according to literature and codes provisions for developing a finite element (FE) model of a case study of a composite deck. The variation of the strength and ductility of the connection is implemented in the numerical model carrying out nonlinear analyses. The results confirm the utility of the model to evaluate the importance of the studs capacity, ductility and strength, on the global response (ductility and strength) of the structures but also to analyse the trend of slip and shear at interface along the beams.

Keywords: Shear Load, slip, steel-concrete composite bridge, stud connectors.

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Authors: Alberto Abello Moreno-Cid

Abstract:

Mummification was the process through which immortality was granted to the deceased, so it was of extreme importance to the Egyptians. The techniques of embalming had evolved over the centuries, and specialists created increasingly sophisticated tools. However, due to its eminently religious nature, knowledge about everything related to this practice was jealously preserved, and the testimonies that have survived to our time are scarce. For this reason, embalming instruments found in archaeological excavations are uncommon. The tomb of the Vizier Amenhotep Huy (AT No. -28-), located in the el-Assasif necropolis that is being excavated since 2009 by the team of the Institute of Ancient Egyptian Studies, has been the scene of some discoveries of this type that evidences the existence of mummification practices in this place after the New Kingdom. The clysters or enemas are the fundamental tools in the second type of mummification described by the historian Herodotus to introduce caustic solutions inside the body of the deceased. Nevertheless, such objects only have been found in three locations: the tomb of Ankh-Hor in Luxor, where a copper enema belonged to the prophet of Ammon Uah-ib-Ra came to light; the excavation of the tomb of Menekh-ib-Nekau in Abusir, where was also found one made of copper; and the excavations in the Bucheum, where two more artifacts were discovered, also made of copper but in different shapes and sizes. Both of them were used for the mummification of sacred animals and this is the reason they vary significantly. Therefore, the object found in the tomb No. -28-, is the first known made of faience of all these peculiar tools and the oldest known until now, dated in the Third Intermediate Period (circa 1070-650 B.C.). This paper bases its investigation on the study of those parallelisms, the material, the current archaeological context and the full analysis and reconstruction of the object in question. The key point is the use of faience in the production of this item: creating a device intended to be in constant use seems to be a first illogical compared to other samples made of copper. Faience around the area of Deir el-Bahari had a strong religious component, associated with solar myths and principles of the resurrection, connected to the Osirian that characterises the mummification procedure. The study allows to refute some of the premises which are held unalterable in Egyptology, verifying the utilization of these sort of pieces, understanding its way of use and showing that this type of mummification was also applied to the highest social stratum, in which case the tools were thought out of an exceptional quality and religious symbolism.

Keywords: Clyster, el-Assasif, embalming, faience enema, mummification, Theban necropolis.

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

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The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: Conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums.

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Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: Kanita Thanacharoenchanaphas, Orose Rugchati

Abstract:

This study assessed the effects of climate change on Thai soybeans under simulation situations. Our study is focused on temperature variability and effects on growth, yield, and genetic changes in 2 generations of Chiang Mai 60 cultivars. In the experiment, soybeans were exposed to 3 levels of air temperature for 8 h day-1 in an open top chamber for 2 cropping periods. Air temperature levels in each treatment were controlled at 30-33°C (± 2.3) for LT-treatment, 33-36°C ( ± 2.4) for AT-treatment, and 36-40 °C ( ± 3.2) for HT-treatment, respectively. Positive effects of high temperature became obvious at the maturing stage when yield significantly increased in both cropping periods. Results in growth indicated that shoot length at the pre-maturing stage (V3-R3) was more positively affected by high temperature than at the maturing stage. However, the positive effect on growth under high temperature was not found in the 2nd cropping period. Finally, genetic changes were examined in phenotype characteristics by the AFLPs technique. The results showed that the high temperature factor clearly caused genetic change in the soybeans and showed more alteration in the 2nd cropping period.

Keywords: simulation, air temperature, variability, Thai soybean, yield , genetic change

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Authors: Samra Bajwa, Muhammad W. Siddiqi

Abstract:

The study investigates the causal link between trade openness and economic growth for four South Asian countries for period 1972-1985 and 1986-2007 to examine the scenario before and after the implementation of SAARC. Panel cointegration and FMOLS techniques are employed for short run and long run estimates. In 1972-85 short run unidirectional causality from GDP to openness is found whereas, in 1986-2007 there exists bi-directional causality between GDP and openness. The long run elasticity magnitude between GDP and openness contains negative sign in 1972-85 which shows that there exists long run negative relationship. While in time period 1986-2007 the elasticity magnitude has positive sign that indicates positive causation between GDP and openness. So it can be concluded that after the implementation of SAARC overall situation of selected countries got better. Also long run coefficient of error term suggests that short term equilibrium adjustments are driven by adjustment back to long run equilibrium.

Keywords: Causality, Economic Growth, Panel Co-integration, SAARC, Trade Openness.

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Authors: Zuzana Poborilova, Anna B. Ohlsson, Torkel Berglund, Anna Vildova, Petr Babula

Abstract:

Lawsone is a pigment that occurs naturally in plants. It has been used as a skin and hair dye for a long time. Moreover, its different biological activities have been reported. The present study focused on the effect of lawsone on a plant cell model represented by tobacco BY-2 cell suspension culture, which is used as a model comparable with the HeLa cells. It has been shown that lawsone inhibits the cell growth in the concentration-dependent manner. In addition, changes in DNA methylation level have been determined. We observed decreasing level of DNA methylation in the presence of increasing concentrations of lawsone. These results were accompanied with overproduction of reactive oxygen species (ROS). Since epigenetic modifications can be caused by different stress factors, there could be a connection between the changes in the level of DNA methylation and ROS production caused by lawsone.

Keywords: DNA methylation, Lawsone, Naphthoquinone, Reactive Oxygen Species.

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Authors: E. Kouhgardi, S. Dashti, H. Fekrandish

Abstract:

This research has been conducted to study the method of culture and comparing growth and biomass of Gracilaria corticata cultured on rope and net for 50 days through two treatments (first treatment: culture of alga on net and the second treatment: culture of alga on rope and each treatment was repeated by four cases). During culture period, the water of aquariums was replaced once every two days for 40-50%. Also, 0.3-0.5 grams of urea fertilizer was added to the culture environment for fertilization. Moreover, some of the environmental factors such as pH, salinity and temperature of the environment were measured on a daily basis. During the culture period, extent of longitudinal growth of the species of both treatments was equal. The said length was reached from 8-10 cm to 10.5-13 cm accordingly. The resulted weight in repetitions of the first treatment was higher than that of the second treatment in such a way as in the first treatment, its weight reached from 10 grams to 21.119 grams and in the second treatment, its weight reached from 10 grams to 17.663 grams. On a whole, it may be stated that that kind of alga being studied has a considerable growth with respect to its volume. The results have revealed that the percentage of daily growth and wet weight at the end of the first treatment was higher than that of the second treatment and it was registered as 0.934, 6.072 and 811.432 in the first treatment and 0.797, 4.990 and 758.071 in the second treatment respectively. This difference is significant (P<0.05). Growth and biomass of G. corticata through culture on net was more emphasizing on numerous branches due to wider bed. Moreover, higher level of the species in this method was exposed to sunlight and this increased biosynthesis and eventually increases of growth and biomass.

Keywords: Red alga, growth, biomass, culture, net, rope.

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Authors: Mohammad Asif

Abstract:

An accurate prediction of the minimum fluidization velocity is a crucial hydrodynamic aspect of the design of fluidized bed reactors. Common approaches for the prediction of the minimum fluidization velocities of binary-solid fluidized beds are first discussed here. The data of our own careful experimental investigation involving a binary-solid pair fluidized with water is presented. The effect of the relative composition of the two solid species comprising the fluidized bed on the bed void fraction at the incipient fluidization condition is reported and its influence on the minimum fluidization velocity is discussed. In this connection, the capability of packing models to predict the bed void fraction is also examined.

Keywords: Bed void fraction, Binary solid mixture, Minimumfluidization velocity, Packing models

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: Algebras over integral domains, Alexandroff topology, valuation domains, integral domains.

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