Exchange Symmetries in Motzkin Path and Bargraph Models of Copolymer Adsorption
نویسندگان
چکیده
In a previous work [26], by considering paths that are partially weighted, the generating function of Dyck paths was shown to possess a type of symmetry, called an exchange relation, derived from the exchange of a portion of the path between weighted and unweighted halves. This relation is particularly useful in solving for the generating functions of certain models of vertex-coloured Dyck paths; this is a directed model of copolymer adsorption, and in a particular case it is possible to find an asymptotic expression for the adsorption critical point of the model as a function of the colouring. In this paper we examine Motzkin path and partially directed walk models of the same adsorbing directed copolymer problem. These problems are an interesting generalisation of previous results since the colouring can be of either the edges, or the vertices, of the paths. We are able to find asymptotic expressions for the adsorption critical point in the Motzkin path model for both edge and vertex colourings, and for the partially directed walk only for edge colourings. The vertex colouring problem in partially directed walks seems to be beyond the scope of the methods of this paper, and remains an open question. In both these cases we first find exchange relations for the generating functions, and use those to find the asymptotic expression for the adsorption critical point.
منابع مشابه
Removal of Methylene Blue from Water by Polyacrylonitrile Co Sodium Methallylsulfonate Copolymer (AN69) and Polysulfone (PSf) Synthetic Membranes
Polyacrylonitrile-co-sodium methallylsulfonate copolymer (AN69) and polysulfone (PSf) synthetic membranes were prepared and used for the removal of methylene blue (MB) from water. Atomic Force Microscopy (AFM), Ionic exchange capacity (IEC), and Swelling ratio (Sr) were employed to determine the membrane characteristics. pH, membrane composition and initial dye concentration were used for t...
متن کاملAdsorption of Cr(III) and Mg(II) from Hydrogen Peroxide Aqueous Solution by Amberlite IR-120 Synthetic Resin
In concentration of hydrogen peroxide, first, the solution should be quite pure, and then, it concentrate with methods such as vacuum distillation and cooling crystallization, because impurities in the hydrogen peroxide solution in high concentrations are causing decomposition of this substance; that is very dangerous. The purpose of this article is separation of chromium and magne...
متن کاملAdsorptive Removal of Al, Zn, Fe, Cr and Pb from Hydrogen Peroxide Solution by IR-120 Cation Exchange Resin
Adsorption of cations Al, Zn, Fe, Cr and Pb from aqueous solution of hydrogen peroxide using IR-120 cation-exchange resin was studied. The removal percentage of the cations was examined by varying experimental conditions (such as pH of the hydrogen peroxide solution, temperature, contact time and dosage of adsorbent) i...
متن کاملStudying effects of ion exchange resin structure and functional groups on Re(VII) adsorption onto Purolite A170 and Dowex 21K
The effects of the functional groups and structures of two different resins, weak base/macroporous and strong base/gel type, Purolite A170 and Dowex 21K on the adsorption properties of Re(VII) ions were investigated experimentally and described by the isotherm, kinetic, and thermodynamic modeling. In this regard, four widely used adsorption isotherm models including Langmuir, Freundlich, Temkin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 9 شماره
صفحات -
تاریخ انتشار 2002