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This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications  

To a hyperbolic smooth curve defined over a number-field one naturally associates "ananabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than those coming from deformations of "abelian" Galois representations induced by the Tate module of associated Jacobian variety. We develop an arithmetic deformation theory of graded Lie algebras with finite dimensional graded components to serve our purpose  

By Grothendieck’s anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number-fields encode all the arithmetic information of these curves. The Goal of this paper is to develop an arithmetic Teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number-fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework. © 2019 Academic Center for Education, Culture and Research TMU  

By Grothendieck’s anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number-fields encode all the arithmetic information of these curves. The Goal of this paper is to develop an arithmetic Teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number-fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework. © 2019 Academic Center for Education, Culture and Research TMU  

Let p be a prime not dividing the integer n. By an Ihara result, we mean existence of a cokernel torsion-free injection from a full lattice in the space of p-old modular forms into a full lattice in the space of all modular forms of level pn. In this paper, we will prove an Ihara result in the number field case, for Siegel modular forms. The case of elliptic modular forms is discussed in Ihara (Discrete subgroups of Lie groups and applications to moduli, Oxford University Press, Bombay, 1975). We will use a geometric formulation for the notion of p-old Siegel modular forms (Rastegar in BIMS 43(7):1–23, 2017). Then, we apply an argument by Pappas, and prove the Ihara result using density of... 

Let p be a prime number and let n be a positive integer prime to p. By an Ihara-result, one means the existence of an injection with torsion-free cokernel, from a full lattice, in the space of p-old modular forms, into a full lattice, in the space of all modular forms of level np. In this paper, Ihara-results are proven for genus two Siegel modular forms, Siegel-Jacobi forms and Hilbert modular forms. Ihara did the genus one case of elliptic modular forms [1]. A geometric formulation is proposed for the notion of p-old Siegel modular forms of genus two, using clarifying comments by R. Schmidt [2] and, then, following suggestions in an earlier paper [3] on how to prove Ihara results. The main... 

Despite the economic and environmental advantages of plug-in hybrid electric vehicles (PHEVs), the increased utilization of PHEVs brings up new concerns for power distribution system decision makers. Impacts of PHEVs on distribution networks, although have been proven to be noticeable, have not been thoroughly investigated for future years. In this paper, a comprehensive model is proposed to study the PHEV impacts on residential distribution systems. In so doing, PHEV fundamental characteristics, i.e., PHEV battery capacity, PHEV state of charge (SOC), and PHEV energy consumption in daily trips, are accurately modeled. As some of these effective characteristics depend on vehicle owner's... 

This paper presents a residential energy hub model for a smart multi-carrier energy home consisting of plug-in hybrid electric vehicle (PHEV), combined heat and power (CHP), solar panels, and electrical storage system (ESS). The energy hub inputs are electricity and natural gas that provide electrical and heat demands at the output ports. In this paper, an optimization-based program is proposed to determine the optimal operation mode of the energy hub, to manage the energy consumption of responsive appliances, to schedule charging/discharging of PHEV and the storage system, and to coordinate solar panels operation with household responsive demand in response to day-ahead time-varying tariffs... 

This paper proposes a novel optimization based home load control (HLC) to manage the operation periods of responsive electrical appliances, determine several recommended operation periods for nonresponsive appliances, and schedule the charge/discharge cycling of plug-in hybrid electric vehicle (PHEV) considering various customer preferences. The customer preferences are in the format of payment cost, interruption cost, and different operational constraints. The projected algorithm is online, in which household appliances are initially scheduled based on the payment cost, and when the home load is interrupted, the scheduling will be updated to minimize customer interruption cost. Due to...