The topology of fullerenes

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website

Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Square Graphs

في البيان المتصل G، دالة المسافة بين أي رأسين من رؤوس البيان  هي أقصر مسافة بينهما، كما تعرف درجة الرأس  والتي يرمز لها بـ  بأنها عدد الحافات الواقعة عليه. متعددة حدود شوالتز وشوالتز المعدلة تعرف كالاتي:   على التوالي، حيث أن المجموع يؤخذ لكل الازواج غير المرتبة من الرؤوس المختلفة في  وأن  هي المسافة بين الرأسين   و  في . في هذا البحث استطعنا الحصول على صيغ عامة لكل من متعددة حدود شوالتز وشوالتز المعدلة ودليليهما ومعدلهما لتطابق الحافة لسلسلة وحلقة للبيانات المربعة.  In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:  respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work

Kinetic and Thermodynamic Studies of Charge-Transfer Complex Formation between Imipramine and 2,3-Dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) in Acetonitrile and Dichloromethane Solutions

Spectro-kinetic studies revealed the formation of charge-transfer (CT) complex of imipramine as an electron donor with π acceptor 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) in acetonitrile and dichloromethane solutions. The resulted CT complexes exhibit spectra that were remarkably different fromthose of the donor and acceptor. The stoichiometry of the resulting complex was found to be 1:1 by the method of Job‘s continuous variation. The formation constants and thermodynamic parameters of the resulting electron-donor-acceptor (DA) complexes were determined by Benesi-Hildebrand and van’t Hoff equations, respectively. The time-dependent spectra recorded after mixing donor and acceptor has been related to an immediate formation of DA complex, which is followed by two relatively slow consecutive reactions. The pseudo-first-order rate constants for the formation of the ionic intermediate and the final product have been evaluated at various temperatures by computer fitting of the absorbance-time data to appropriate equations. The activation parameters, i.e. activation energy, enthalpy, and entropy of activation were computed from temperature dependence of the rate constants. The observed results afford evidence concerning the critical role of solvent polarity on the kinetics and stability of the resulting charge transfer complexes. The ionization potential of the donor in the two solvents was estimated and compared with the theoretical values.KEYWORDS Charge-transfer complex, imipramine, DDQ, ionization potential, kinetic, thermodynamic

Application of Topological Indices of Tenofovir Chemical Structures for the Cure of HIV/AIDS Patients

Human immune deficiency virus (HIV), a retrovirus, is the main reason for acquired immune deficiency syndrome (AIDS), and one of the prime social and medical problems at the present time. Approximately around 100 million citizens all over the world are suffering from HIV virus and around 50 million citizens are dead. This virus expanded rapidly all over the world. Unfortunately, there is no medicine, drug or vaccine is identified to treat this virus. Scientists have recognised the effectiveness of already existing anti-viral drugs to cure and control the HIV virus. Some of them are Tri-POC Tenofovir Dimer, Tenofovir Disproxil and Tenofovir Alafenamide.Topological indices- mathematical elucidations for a molecule can be created by an algorithm and can be applied to its representation. To generate various biological and physicochemical properties of chemical compounds, topological indices are used. In the current study, by using polynomial approach, for the above mentioned antiviral drugs, certain neighbourhood sum& degree based topological indices have been studied. The outcomes achieved can support the invention of new medicine for the cure of AIDS. In the present study, we establish some topological properties of Tenofovir dimer, Tenofovir disproxil and alafenamide used to inhibit the outbreak of AIDS. We compute some topological indices (general indices (Randic and harmonic), Zagreb index (1st, 2nd, 3rd, second modified, Redefined 3rdand Augmented), Forgotten index, Systematic division index and Inverse sum indices for these three chemical structures. In Medical Science, topological index calculation defines the topological index related to molecular structure and its corresponding biological, medical, pharmaceutical, and chemical properties of the medicines. From last twenty to thirty years the world is fronting the danger of identifying cure for AIDS. Nearly 10 million people are getting affected with this disease every year. In order to cure this malicious disease antiviral drugs, in form of anti-metabolites, hormones and alkylating agents are used. As per numerous examinations conducted with their chemical structures, it revealed that there is a association between the characteristic features of these anti-viral medicines, drugs and alkane’s viz.enthalpy, melting point and boiling point. In this current study, numerous topological indices have been defined on few of the above mentioned drugs so as to assist the scientists to identify the chemical reactions and physical & chemical characteristics and biological activities that are related with them. Hence, the topological indices study on the molecular structure of the medicines, drugs chemical compounds, can constitute for absence of laboratory research which provides a notional origin for the production of chemical materials and drugs. In the present study, we analysed the Tenofovir family chemicals which is extensively used in antiviral medicines and drugs invention. Eleven topological indices are analysed using multi-order polynomials and these results can be used in medicine and pharmaceutical experiments thus paving the new way for new drug invention for AIDS

Polymer brushes - Wetting properties and my-patterning

In this work polymer brushes on both flat and curved substrates were prepared by grafting from and grafting to techniques. The brushes on flat substrates were patterned on the µm-scale with the use of an inkjet printer. Thus it was demonstrated that chemistry with an inkjet printer is feasible. The inkjet printer was used to deposit microdroplets of acid. The saponification of surface-immobilized ATRP initiators containing an ester bond occurred in these microdroplets. The changes in the monolayer of ester molecules due to saponification were amplified by SI-ATRP. It was possible to correlate the polymer brush thickness to effectiveness of saponification. The use of an inkjet printer allowed for simultaneously screening of parameters such as type of acid, concentration of acid, and contact time between acid and surface. A dip-coater was utilized in order to test the saponification independent of droplet evaporation. The advantage of this developed process is its versatility. It can be applied to all surface-immobilized initiators containing ester bonds. The technique has additionally been used to selectively defunctionalize the initiator molecules covering a microcantilever on one side of a cantilever. An asymmetric coating of the cantilever with polymer brushes was thus generated. An asymmetric coating allows the use of a microcantilever for sensing applications. The preparation of nanocomposites comprised of polyorganosiloxane microgel particles functionalized with poly(ethyl methacrylate) (PEMA) brushes and linear, but entangled, PEMA chains is described in the second major part of this thesis. Measurement of the interparticle distance was performed using scanning probe microscopy and grazing incidence small angle X-ray scattering. The matrix molecular weight at which the nanocomposite showed microphase separation was related to abrupt changes in inter-particle distance. Microphase separation occurred once the matrix molecular exceeded the molecular weight of the brushes. The trigger for the microphase separation was a contraction of the polymer brushes, as the measurements of inter-particle distance have revealed. The brushes became impenetrable for the matrix chains upon contraction and thus behaved as hard spheres. The contraction led to a loss of anchoring between particles and matrix, as shown by nanowear tests using an atomic force microscope. Polyorganosiloxane microgel particles were functionalized with 13C enriched poly(ethyl methacrylate) brushes. New synthetic pathways were developed in order to enrich not the entire brush with 13C, but only exclusively selected regions. 13C chemical shift anisotropy, an advanced NMR technique, can thus be used in order to gather information about the extended conformations in the 13C enriched regions of the PEMA chains immobilized on the µ-gel-g-PEMA particles. The third part of this thesis deals with the grafting to of polymeric fullerene materials on silicon substrates. Active ester chemistry was employed in order to prepare the polymeric fullerene materials and graft these materials covalently on amino-functionalized silicon substrates.rnIn der vorgelegten Arbeit wurde gezeigt, wie es möglich isr Polymerbürsten auf flachen und gekrümmten Oberflächen unter Verwendung von grafting from - und grafting to-Techniken zu synthetisieren. Auf den flachen Oberflächen wurde ein Tintenstrahldrucker dazu benutzt, die Bürsten zu strukturieren. Die dabei erzeugten Strukturen waren von ihrer Größe her im Mikrometerbereich angesiedelt. Dabei wurde zum ersten Mal demonstriert wie ein Tintenstrahldrucker verwendet werden kann, um chemische Reaktionen durchzuführen. Im Speziellen wurde der Tintenstrahldrucker dazu verwendet mikrometergroße Säuretropfen eine Oberfläche aufzubringen. In diesen Tropfen fand eine Esterspaltung in auf der Oberfläche verankerten Molekülen statt, die neben der Estergruppe auch eine Gruppe enthielten, die als Initiator in der ATRP fungieren konnte. Die Änderung in der Monolage dieser Moleküle aufgrund der Esterspaltung führte dazu, dass die Moleküle nicht mehr als ATRP-Initiator fungieren konnten. Mittels einer oberflächeninitiierten ATRP wurden diese Änderungen dann sichtbar gemacht. Dadurch war es möglich, die erhaltene Dicke der Polymerbürsten mit dem Wirkungsgrad der Esterspaltung in Verbindung zu setzen. Der Tintenstrahldrucker erlaubte es somit nicht nur verschiedene Muster auf der Oberfläche zu generieren, sondern auch simultan verschiedene Parameter der Esterspaltung auszutesten, unter anderem die Säureart, die Konzentration der jeweiligen Säure und die Verweildauer der Säure auf der Oberfläche. Dabei wurde festgestellt, dass die Verdampfung der mikrometergroßen Tropfen einen beträchtlichen Einfluss auf die Esterspaltung hat. Daher wurde in weiteren Experimenten ein Dip-Coater dazu benutzt, die Esterspaltung unabhängig von der Verdampfung zu untersuchen. Der Vorteil der entwickelten Methoden ist sicherlich in ihrer Vielseitigkeit zu sehen. Sie kann auf alle auf oberflächenverankerte Initiatormoleküle angewandt werden, so lange sie eine Estergruppe enthalten. Des Weiteren wurde die Methode dazu verwendet, um selektiv auf einer Seite die Initiatormoleküle auf einem Mikrocantilever zu zerstören. Somit wurde eine asymmetrische Beschichtung des Mikrocantilevers erzeugt, welche eine Voraussetzung für den Einsatz eines Mikrocantilevers zur Detektion ist. In zweiten Teil der Arbeit ging es um die Eigenschaften einer Mischung von Mikrogel-Partikeln aus Polyorganosiloxanen, die mit Poly(ethylmethacrylate)-Bürsten beschichtet waren, mit linearen, aber verschlauften PEMA Ketten. Der Abstand der Nanopartikel in dieser Mischung wurde mittels Rastersondenmikroskopie und Kleinwinkelstreuung unter streifendem Einfall untersucht. Anhand des Abstandes der Partikel war es möglich, das Molekulargewicht der Ketten in der Matrix zu ermitteln, oberhalb dessen es zu einer sogenannten Mikrophasen-Separation kommt. Die Mikrophasen-Separation trat auf, sobald das Molekulargewicht der Ketten in der Matrix größer wurde als das Molekulargewicht der Polymerbürsten auf der Oberfläche der Nanopartikel. Als Auslöser für die Mikrophasen-Separation wurde eine Kontraktion der Polymerbürsten identifiziert, wie die Messungen der Partikel-Abstände gezeigt hatten. Die Polymerbürsten wurden unzugänglich für die Ketten in der Matrix, sobald sie kollabiert waren. Somit verhielten sich die Nanopartikel wie harte Kugeln in der Matrix. Die Kontraktion ging mit einem Verlust der Verankerung der Partikel in der Matrix einher. Die Verankerung der Partikel wurde durch Nanowear-Experimente in einem Rastersondenmikroskop untersucht. Die Mikrogel-Partikel aus Polyorganosiloxanen wurden für ein weiteres Projekt mit 13C angereicherten Poly(ethylmethacrylat)-Bürsten beschichtet. Des Weiteren wurden Synthesewege entwickelt, um in ausgewählten Regionen der Polymerbürsten 13C angereicherte Monomeren einzubauen. 13C chemical shift anisotropy, eine hochentwickelte NMR-Methode, wurde dazu verwendet, um die Konformation der Bereiche, die mit 13C angereichert worden waren, selektiv zu untersuchen. Im dritten Teil der Arbeit wurde gezeigt, wie es möglich war mittels einer grafting to-Technik fullerenfuntionalisierte Polymere auf Silzium-Substraten zu verankern. Aktivesterchemie wurde nicht nur dazu verwendet, um die Fulleren-Moleküle kovalent an die Polymerketten anzubinden, sondern auch um die fullerenfunktionalisierten Polymere auf der Oberfläche anzubinden.250 S

Applied and Computational Statistics

Research without statistics is like water in the sand; the latter is necessary to reap the benefits of the former. This collection of articles is designed to bring together different approaches to applied statistics. The studies presented in this book are a tiny piece of what applied statistics means and how statistical methods find their usefulness in different fields of research from theoretical frames to practical applications such as genetics, computational chemistry, and experimental design. This book presents several applications of the statistics: A new continuous distribution with five parameters—the modified beta Gompertz distribution; A method to calculate the p-value associated with the Anderson–Darling statistic; An approach of repeated measurement designs; A validated model to predict statement mutations score; A new family of structural descriptors, called the extending characteristic polynomial (EChP) family, used to express the link between the structure of a compound and its properties. This collection brings together authors from Europe and Asia with a specific contribution to the knowledge in regards to theoretical and applied statistics