Minimal varieties of residuated lattices

In this paper we investigate the atomic level in the lattice of subvarieties of residuated lattices. In particular, we give infinitely many commutative atoms and construct continuum many non-commutative, representable atoms that satisfy the idempotent law; this answers Problem 8.6 of [12]. Moreover, we show that there are only two commutative idempotent atoms and only two cancellative atoms. Finally, we study the connections with the subvariety lattice of residuated bounded-lattices. We modify the construction mentioned above to obtain a continuum of idempotent, representable minimal varieties of residuated bounded-lattices and illustrate how the existing construction provides continuum many covers of the variety generated by the three-element non-integral residuated bounded-lattice.In Celebration of the Sixtieth Birthday of Ralph N. McKenzieReceived August 1, 2003; accepted in final form April 27, 2004.     

Free-space fluorescence molecular tomography utilizing 360 degrees geometry projections

Fluorescence tomography of diffuse media can yield optimal three-dimensional imaging when multiple projections over 360 degrees geometries are captured, compared with limited projection angle systems such as implementations in the slab geometry. We demonstrate how it is possible to perform noncontact, 360 degrees projection fluorescence tomography of mice using CCD-camera-based detection in free space, i.e., in the absence of matching fluids. This approach achieves high spatial sampling of photons propagating through tissue and yields a superior information content data set compared with fiber-based 360 degrees implementations. Reconstruction feasibility using 36 projections in 10 degrees steps is demonstrated in mice.     

Generalized layerwise mechanics for the static and modal response of delaminated composite beams with active piezoelectric sensors

A coupled linear layerwise laminate theory and a beam FE are formulated for analyzing delaminated composite beams with piezoactuators and sensors. The model assumes zig-zag fields for the axial displacements and the electric potential and it treats the discontinuities in the displacement fields due to the delaminations as additional degrees of freedom. The formulation naturally includes the excitation of piezoelectric actuators, their interactions with the composite laminate, and the effect of delamination on the predicted sensory voltage. The quasistatic and modal response of laminated composite Gr/Epoxy beams with active or sensory layers having various delamination sizes is predicted. The numerical results illustrate the strong effect of delamination on the sensor voltage, on through the thickness displacement and on the stress fields. Finally, the effect of delamination on modal frequencies and shapes are predicted and compared with previously obtained experimental results.     

Responsive Copolymer Brushes of Poly[(2‐(Methacryloyloxy)Ethyl) Trimethylammonium Chloride] (PMETAC) and Poly(1H,1H,2H,2H‐Perfluorodecyl acrylate) (PPFDA) to Modulate Surface Wetting Properties

Polymer brushes have a large potential for controlling properties such as surface lubrication or wetting through facile functionalization. Polymer chemistry, chain density, and length impact on the wetting properties of brushes. This study explores the use of diblock copolymer brushes with different block length and spatial arrangement of the blocks to tune surface wettability. Block copolymer brushes of the polyelectrolyte [2‐(methacryloyloxy)ethyl] trimethylammonium chloride (PMETAC) with a contact angle of 17° and a hydrophobic block of ¹H, ¹H, ²H, ²H‐perfluorodecyl Acrylate (PPFDA) with a contact angle of 130° are synthesized by RAFT polymerization. By changing the sequence of polymerization either block is synthesized as top or bottom block. By varying the concentration of initiator the length of the blocks is varied. Contact angle values with intermediate values between 17° and 130° are measured. In addition, by changing solvent pH and in presence of a different salt the contact angle of the copolymer brushes can be fine tuned. Brushes are characterized by atomic force microscopy, Raman confocal microscopy, and X‐ray photoelectron spectroscopy.

     

On p-logistic equations of equidiffusive type

We consider a p-logistic equation with equidiffusive reaction. We study the existence, nonexistence and uniqueness of positive solutions as the parameter \(\lambda >0\) varies. In the case of a unique positive solution \(u_{\lambda }\), we investigate the monotonicity and continuity properties of the map \(\lambda \rightarrow u_{\lambda }\).     

Bounds tightening based on optimality conditions for nonconvex box-constrained optimization

First-order optimality conditions have been extensively studied for the development of algorithms for identifying locally optimal solutions. In this work, we propose two novel methods that directly exploit these conditions to expedite the solution of box-constrained global optimization problems. These methods carry out domain reduction by application of bounds tightening methods on optimality conditions. This scheme is implicit and avoids explicit generation of optimality conditions through symbolic differentation, which can be memory and time intensive. The proposed bounds tightening methods are implemented in the global solver BARON. Computational results on a test library of 327 problems demonstrate the value of our proposed approach in reducing the computational time and number of nodes required to solve these problems to global optimality.     

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and π-institutions

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.     

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).