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Taming Modal Impredicativity: Superlazy Reduction  [PDF]
Ugo Dal Lago,Luca Roversi,Luca Vercelli
Computer Science , 2008,
Abstract: Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing the complexity of cut-elimination to be problematic from a complexity point of view. Modal impredicativity occurs when, during reduction, the conclusion of a residual of a box b interacts with a node that belongs to the proof net inside another residual of b. Technically speaking, superlazy reduction is a new notion of reduction that allows to control modal impredicativity. More specifically, superlazy reduction replicates a box only when all its copies are opened. This makes the overall cost of reducing a proof net finite and predictable. Specifically, superlazy reduction applied to any pure proof nets takes primitive recursive time. Moreover, any primitive recursive function can be computed by a pure proof net via superlazy reduction.
Chattering Reduction Using Variable Boundary Layer Solution in a Class of Nonlinear Variable Structure Systems

LI Junhong,LI Lanjun,YANG Wujiao,

系统科学与数学 , 2008,
Abstract: A new method, variable boundary layer solution, is proposed in this paper for a class of nonlinear variable structure systems to restrain the chattering. The mathematical relationship between the static errors and the width of saturatingproperty is presented. The saturating property with time-varying boundary layer width can be designed through the specification of the static errors, which can not only reduce the chattering in the system but also simultaneously satisfy the specification of the static errors. The simulation results show the validity of themethod.
Spoof polariton enhanced modal density of states in planar nanostructured metallic cavities  [PDF]
P. S. Davids,F. Intravaia,D. A. R. Dalvit
Physics , 2014, DOI: 10.1364/OE.22.012424
Abstract: Spoof surface modes on nanostructured metallic surfaces are known to have tailorable dispersion dependent on the geometric characteristics of the periodic pattern. Here we examine the spoof plasmon dispersion on an isolated grating and a grating-planar mirror cavity configuration. The spoof polariton dispersion in the cavity is obtained using the scattering matrix approach, and the related differential modal density of states is introduced to obtain the mode dispersion and classify the cavity polariton modes. The grating-mirror cavity geometry is an example of periodically nanostructured metals above a planar ground plane. The properties discussed here are relevant for applications ranging from thin electromagnetic perfect absorbers to near-field radiative heat transfer.
Modal Coupling Coefficients and Frequency/Bias Planes for Gyromagnetic Boundary Value Problems
Junaid Zafar,Haroon Zafar
International Journal of Electrical and Computer Engineering , 2012, DOI: 10.11591/ijece.v2i5.222
Abstract: In this paper, electromagnetic and uniform precession magnetostatic mode interaction theory is reformulated to include comprehensive electromagnetic modal impact in the determination of modal coupling calculations. For this purpose orthogonal electromagnetic and normal magnetostatic modes character is solved with coupled field Maxwell’s equations and vectorized magnetization expression to model the interactions between electromagnetic modes and magnetostatic uniform precession mode. Calculations for modal coupling factors are presented here for the first time and frequency/ bias planes are constructed using the developed modal interaction formulation with an ameliorated accuracy. The proposed formulation is validated and tested against closed form frequency/ bias solutions concerning these gyromagnetic boundary value problems.
Boundary reduction formula  [PDF]
Z. Bajnok,G. Bohm,G. Takacs
Physics , 2002, DOI: 10.1088/0305-4470/35/44/304
Abstract: An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to the Green functions via the boundary reduction formula derived. The definition of the $R$-matrix for integrable theories due to Ghoshal and Zamolodchikov and the one used in the perturbative approaches are shown to be related.
Limits of Modal Insensitivity for Laser Vibrometry, spectral reduction requires super-symmetry  [PDF]
Michael C. Kobold
Physics , 2014,
Abstract: Lab measurements showed that identification (ID) and monitoring of objects using remote sensing of their vibration signatures are limited in a couple rare cases. This work provides two necessary conditions to infer that the identification of practical targets to within prescribed bounds; failure to ID the spectrum is shown to be rare. Modal modulation of laser return produces data clusters for adequate spectral ID using slowly swept sine (SSS) and small deflection multi-modal (MM) analyses. Results using these completely different calculations lead to practical removal of a remote sensing concern, spectral "reduction" (SR) of return used for object ID. The optical return provides structural mode ID for non-imaging detection and classification. Calculations using a large spot size to completely paint the vibrating object provide insight for SR found in laboratory measurements which use spot size as a variable. Non-imaging calculations comparing SSS and MM approximations show vibrating rectangular plates have spatially integrated (non-imaging) return that varies substantially among low-frequency vibration modes. The clustering of data from these two methods are the necessary conditions for ID. Theories for SSS and MM describe the signal processing physics for a modal recognition capability and how pure one-dimensional modal targets and super-symmetric square plates can frustrate classification.
Reduction of Many-valued into Two-valued Modal Logics  [PDF]
Zoran Majkic
Mathematics , 2011,
Abstract: In this paper we develop a 2-valued reduction of many-valued logics, into 2-valued multi-modal logics. Such an approach is based on the contextualization of many-valued logics with the introduction of higher-order Herbrand interpretation types, where we explicitly introduce the coexistence of a set of algebraic truth values of original many-valued logic, transformed as parameters (or possible worlds), and the set of classic two logic values. This approach is close to the approach used in annotated logics, but offers the possibility of using the standard semantics based on Herbrand interpretations. Moreover, it uses the properties of the higher-order Herbrand types, as their fundamental nature is based on autoreferential Kripke semantics where the possible worlds are algebraic truth-values of original many-valued logic. This autoreferential Kripke semantics, which has the possibility of flattening higher-order Herbrand interpretations into ordinary 2-valued Herbrand interpretations, gives us a clearer insight into the relationship between many-valued and 2-valued multi-modal logics. This methodology is applied to the class of many-valued Logic Programs, where reduction is done in a structural way, based on the logic structure (logic connectives) of original many-valued logics. Following this, we generalize the reduction to general structural many-valued logics, in an abstract way, based on Suszko's informal non-constructive idea. In all cases, by using developed 2-valued reductions we obtain a kind of non truth-valued modal meta-logics, where two-valued formulae are modal sentences obtained by application of particular modal operators to original many-valued formulae.
Modal Decoupling Using the Method of Weighted Residuals for the Nonlinear Elastic Dynamics of a Clamped Laminated Composite
Xiaoling He
Mathematical Problems in Engineering , 2009, DOI: 10.1155/2009/972930
Abstract: We develop an approach to reduce the governing equation of motion for the nonlinear vibration of a clamped laminated composite to the Duffing equation in a decoupled modal form. The method of weighted residuals enables such a reduction for laminates with clamped boundary conditions. Both rigidly clamped and loosely clamped boundary conditions are analyzed using this method. The reduction method conserves the total energy of the system. The decoupled modal form Duffing equation has constant modal parameters in terms of the laminated composite material's properties and geometries. The numerical computations illustrate the individual modal response with an emphasis of the transitional phenomena to chaos caused by the large load.
Bloch wave deafness and modal conversion at a phononic crystal boundary
Vincent Laude,Rayisa P. Moiseyenko,Sarah Benchabane,Nico F. Declercq
AIP Advances , 2011, DOI: 10.1063/1.3675828
Abstract: We investigate modal conversion at the boundary between a homogeneous incident medium and a phononic crystal, with consideration of the impact of symmetry on the excitation of Bloch waves. We give a quantitative criterion for the appearance of deaf Bloch waves, which are antisymmetric with respect to a symmetry axis of the phononic crystal, in the frame of generalized Fresnel formulas for reflection and transmission at the phononic crystal boundary. This criterion is used to index Bloch waves in the complex band structure of the phononic crystal, for directions of incidence along a symmetry axis. We argue that within deaf frequency ranges transmission is multi-exponential, as it is within frequency band gaps.
Prajakta A. Maygaonkar 1 and Usha Permeswaran
Bioscience Discovery , 2012,
Abstract: In the present work biodegradation ability of Aspergillus nidulans have been evaluated for 24 hours of time interval. The effluent was collected from Sanjivani distillery industry located at Kopergaon, Dist Ahemadnagar (M.S) India. Aspergillus nidulans was isolated from soil sample collected from Bhavan’s College campus and purified by serial soil dilution method. Aspergillus nidulans was found to reduce the metallic constituents of effluent such as sodium (Na) and magnesium (Mg) dynamically. Reduction was noticed at 4hrs, 8hrs, 12hrs, and 24 hours of time interval. Much well reduction was noticed when sucrose (1% w/v) and dextrose (1% w/v) were supplemented in effluent. Addition of sucrose showed significant reduction (P< 0.05) for magnesium (Mg) when compare with dextrose. For sodium (Na), less significant result (P< 0.1) was noticed in 24 hours in both experimental flasks containing sucrose and dextrose.
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