Some properties on the tensor product of graphs obtained by monogenic semigroups

Akgunes, N.,Das, K.Ch.,Sinan Cevik, A. Elsevier [etc.] 2014 Applied Mathematics and Computation Vol.235 No.-

In Das et al. (2013) [8], a new graph Γ(S<SUB>M</SUB>) on monogenic semigroups S<SUB>M</SUB> (with zero) having elements {0,x,x<SUP>2</SUP>,x<SUP>3</SUP>,...,x<SUP>n</SUP>} has been recently defined. The vertices are the non-zero elements x,x<SUP>2</SUP>,x<SUP>3</SUP>,...,x<SUP>n</SUP> and, for 1≤i,j≤n, any two distinct vertices x<SUP>i</SUP> and x<SUP>j</SUP> are adjacent if x<SUP>i</SUP>x<SUP>j</SUP>=0 in S<SUB>M</SUB>. As a continuing study, in Akgunes et al. (2014) [3], it has been investigated some well known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Γ(S<SUB>M</SUB>). In the light of above references, our main aim in this paper is to extend these studies over Γ(S<SUB>M</SUB>) to the tensor product. In detail, we will investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the tensor product of any two (not necessarily different) graphs Γ(S<SUB>M</SUB><SUP>1</SUP>) and Γ(S<SUB>M</SUB><SUP>2</SUP>).

Some graph theoretical properties over zero-divisor graphs of special finite commutative rings

N. Akgunes,M. Togan 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.2

Let R be a commutative ring with identity and let Z(R) be the set of zero-divisors of R. It has been widely studied the notion of the zero-divisor graph of R which is de…ned by Γ(R) = Z(R) / {0} such that the distinct vertices x and y are adjacent if and only if xy = 0. As main results of this paper, by considering R = Z_p x Z_q for di¤erent primes p and q, we prove some graph theoretical properties over Γ(Z_p x Z_q) which are the generalizations of the results in [12].

On the first Zagreb index and multiplicative Zagreb coindices of graphs

Das, Kinkar Ch.,Akgunes, Nihat,Togan, Muge,Yurttas, Aysun,Cangul, I. Naci,Cevik, A. Sinan De Gruyter Open 2016 Analele Stiintifice ale Universitatii Ovidius Cons Vol.24 No.1

<P>For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.</P>

Stepped Impedance Resonators for High-Field Magnetic Resonance Imaging

Akgun, Can E.,DelaBarre, Lance,Yoo, Hyoungsuk,Sohn, Sung-Min,Snyder, Carl J.,Adriany, Gregor,Ugurbil, Kamil,Gopinath, Anand,Vaughan, J. Thomas IEEE 2014 IEEE Transactions on Biomedical Engineering Vol.61 No.2

<P>Multi-element volume radio-frequency (RF) coils are an integral aspect of the growing field of high-field magnetic resonance imaging. In these systems, a popular volume coil of choice has become the transverse electromagnetic (TEM) transceiver coil consisting of microstrip resonators. In this paper, to further advance this design approach, a new microstrip resonator strategy in which the transmission line is segmented into alternating impedance sections, referred to as stepped impedance resonators (SIRs), is investigated. Single-element simulation results in free space and in a phantom at 7 T (298 MHz) demonstrate the rationale and feasibility of the SIR design strategy. Simulation and image results at 7 T in a phantom and human head illustrate the improvements in a transmit magnetic field, as well as RF efficiency (transmit magnetic field versus specific absorption rate) when two different SIR designs are incorporated in 8-element volume coil configurations and compared to a volume coil consisting of microstrip elements.</P>

APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS

Akgun Ramazan,Israfilov Daniyal M. Korean Mathematical Society 2006 대한수학회지 Vol.43 No.2

Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

Assessment of Color Strength and Color Difference Values of Polyester Fabrics Containing Continuous Weft Yarns after Abrasion

Akgun, Mine,Becerir, Behcet,Alpay, Halil Rifat The Korean Fiber Society 2007 Fibers and polymers Vol.8 No.5

This paper assesses the color difference and color strength values (K/S) obtained for eight disperse-dyed polyester fabric samples with different fabric construction parameters (weft yarn type, weft yarn count, weft density and fabric weave) after four sets of abrasion cycles. Warp yarn type and count, warp density, and warp yarn twist are the same for all fabrics. Fabric samples are dyed in a commercial red disperse dye (C.I. Disperse Red 74:1) and four different abrasion cycles (2500, 5000, 7500, 10000) are used. The K/S values of the abraided fabrics and color difference values between the control fabric (dyed but not abraided) and abraded fabrics are calculated. The main differences in the K/S and color difference values are observed between 0-2500 abrasion cycles. The high tenacity of the polyester fibers and continuous polyester yams causes some fuzz but no pilling formation on the fabric surface that lead to increased K/S values and color differences. Fiber dullness, yarn thickness, yarn density and fabric weave are concluded to have different effects on the appearance after abrasion.

Series D : Misunderstandings and Difficulties in Learning Sequence and Series: A Case Study

( Akgun Levent ),( Duru Adem ) 한국수학교육학회 2007 수학교육연구 Vol.11 No.1

Temperature Changes in Superficial and Deep Tissue Layers with Respect to Time of Cold Gel Pack Appliaction in Dogs

Kenan Akgun,Mehmet Ali Korpinar,Mustafa Tunaya Kalkan,Ulku Akarirmak,Sansin Tuzun,Fikret Tuzun 연세대학교의과대학 2004 Yonsei medical journal Vol.45 No.4

Despite the widespread clinical use of cryotherapy, there is only limited and inconsistent data on application times. The aim of this study was to determine the changes in tissue temperature and the duration of this effect. In this experimental study, five adult dogs were used. A cold gel pack (10×20 cm) was applied transversally over the right leg femoral region. Temperatures were recorded simultaneously: rectal by a mercury thermometer; right leg skin by probe of Nihon Kohden 6000 polygraph; and right leg subcutaneous, intramuscular, and periosteal, and left leg intramuscular temperatures by a fluorooptic biomedical fiber optic (0.6mm diameter) thermometer connected to a computer system. Total system accuracy was 0.01℃. Cold gel packs were applied for 10, 15, 20, 25, and 30 minutes duration. The results can be summarized as cooling and rewarming data. 1) The superficial tissues such as skin and subcutaneous demonstrated the most rapid and profound cooling effect. The deeper tissues such as bone and muscle exhibited a smaller and more gradual decline in temperature. 2) There was a prolonged rewarming period in all tissues after the removal of the cold gel pack but this period was longer in deeper tissues. According to cold gel pack application time, the rewarming time in intramuscular layers to baseline or plateau temperatures was about: 60± 3 minutes for 10 minutes application, 100±4 for 15, 130±5 for 20, 140±7 for 25, and 145±8 for 30. It can be concluded from these results that with increased cold gel pack application time, deep tissue temperature decreased and the duration of cooling effect increased. However, the data indicated that the length of application time and the duration of cooling effect were not linearly related. Especially after 20 minutes of application this ratio decreased progressively. There may be implications of these results for clinical practice.

Hopelessness, Depression and Social Support with End of Life Turkish Cancer Patients

Sahin, Zumrut Akgun,Tan, Mehtap,Polat, Hatice Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.5

Background: This study was performed to evaluate relationships between different demographic variables and hopelessness and depression in end of life Turkish cancer patients. This study was a descriptive survey with repeated measures conducted a university hospital in the city of Erzurum, in the eastern part of Turkey. The study enrolled 216 patients undergoing palliative treatment at the hospital. Materials and Methods: Data were collected using questionnaires (demographic questionnaire, Beck Hopelessness Scale (BHS), Beck Depression Scale (BDS) and analyzed for demographic and disease-related variable effects on hopelessness and depression. Results: Th hopelessness score was significantly high in female, illiterate, married, and living in rural areas cancer patients. Both hopelessness and depression scores were significantly higher with longer disease duration, receiving radiotherapy treatment, and having metastatic disease. Conclusions: These findings demonstrate the coexistence of the physical, psychological, and cognitive problems faced by patients with cancer. Nurses can conduct brief screening assessments to identify patients with probable distress and and psychosocial support, as well as referrals to support services.

Controlled Release fromModel Blend Multilayer FilmsContaining Mixtures of Strong and Weak Polyelectrolytes

Jang, Yeongseon,Akgun, Bulent,Kim, Hosub,Satija, Sushil,Char, Kookheon American ChemicalSociety 2012 Macromolecules Vol.45 No.8

<P>We have designed the controlled release platforms basedon polyelectrolyte(PE) blend multilayer films to investigate the release mode and kineticsat the nanoscale level. The model blend multilayer films are composedof positively charged layers with weak polyelectrolytes (PEs) (linearpoly(ethylenimine), LPEI) and negatively charged blend layers withmixtures of strong (poly(sodium 4-styrenesulfonic acid), PSS) andweak (poly(methacrylic acid), PMAA) PEs. The blend multilayer films([LPEI/PSS:PMAA]<SUB><I>n</I></SUB>) with well-defined internalstructure were prepared by the spin-assisted layer-by-layer (LbL)deposition method. Release properties of the multilayer films weresystematically studied as a function of blend ratio by neutron reflectivity(NR), ellipsometer, AFM, FT-IR spectroscopy, and quartz crystal microbalancewith dissipation (QCM-D). Since PSS strong PEs serve as robust skeletonswithin the multilayer films independent of external pH variation,the burst disruption of pure weak PE multilayer films was dramaticallysuppressed, and the release kinetics could be accurately controlledby simply changing the PSS content within the blend films. These releaseproperties of blend multilayer films form the basis for designingthe controlled release of target active materials from surfaces.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/mamobx/2012/mamobx.2012.45.issue-8/ma3002615/production/images/medium/ma-2012-002615_0010.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/ma3002615'>ACS Electronic Supporting Info</A></P>