Irreducible Points Research Articles

Works of Art and the Future

Will adding an artistic layer to our future exercises eventually improve them? Why? How? Will this supposed improvement contribute to the entire exercise or only to some of its aspects? Moreover, will such an improvement have long-term, stable consequences or only momentary and occasional ones? The research question I would like to unfold may then be summarized by the claim “Works of art as gates to the future.” Unsurprisingly, this claim needs further qualifications, such as works of are always/often/occasionally/rarely/never gates to possible/preferable/obnoxious future. Furthermore, what does it mean to be a “gate to the future”? To make the future visible? To make the future understandable? To pave the way toward the future? This vast array of preliminary qualifications suggests that the question of the connection between works of art and the future is awfully tangled. I would be satisfied if this paper provides a frame to be eventually improved by subsequent works. Specifically, I would be happy to explain the first, basic question: why works of art may eventually improve futures exercises. I will focus primarily on Nicolai Hartmann, and secondarily on Roman Ingarden and Ernst Bloch. The conclusion I shall arrive at is that works of art can definitely improve futures exercises, because both aesthetic objects and the futures are unreal objects and presents irreducible points of indeterminateness.

Harmonic fingerprint of unconventional superconductivity in twisted bilayer graphene

Microscopic details such as interactions and Fermiology determine the structure of superconducting pairing beyond the spatial symmetry classification along irreducible point group representations. From the effective pairing vertex, the pairing wave function related to superconducting order unfolds in its orbital-resolved Fourier profile which we call the harmonic fingerprint (HFP). The HFP allows to formulate a concise connection between microsopic parameter changes and their impact on superconductivity. From a random phase approximation analysis of twisted bilayer graphene (TBG) involving $d+id$, $s_{\pm}$, and $f$-wave order, we find that nonlocal interactions, which unavoidably enter the low-energy electronic description of TBG, not only increase the weight of higher lattice harmonics but also have a significant effect on the orbital structure of these pairing states. For gapped unconventional superconducting order such as $s_{\pm}$ and $d+id$, a change in HPF induces enhanced gap anisotropies. Experimental implications to distinguish the different gaps and HPFs are also discussed.

Flow equivalence of sofic shifts

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients.

Flow equivalence of sofic shifts

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients.

Hermitian metrics on F-manifolds

An $F$-manifold is complex manifold with a multiplication on the holomorphic tangent bundle with a certain integrability condition. Important examples are Frobenius manifolds and especially base spaces of universal unfoldings of isolated hypersurface singularities. This paper reviews the construction of hermitian metrics on $F$-manifolds from $tt^*$ geometry. It clarifies the logic between several notions. It also introduces a new {\it canonical} hermitian metric. Near irreducible points it makes the manifold almost hyperbolic. This holds for the singularity case and will hopefully lead to applications there.

On the Number of Irreducible Points in Polyhedra

An integer point in a polyhedron is called irreducible iff it is not the midpoint of two other integer points in the polyhedron. We prove that the number of irreducible integer points in $n$-dimensional polytope with radius $k$ given by a system of $m$ linear inequalities is at most $O(m^{\lfloor\frac{n}{2}\rfloor}\log^{n-1} k)$ if $n$ is fixed. Using this result we prove the hypothesis asserting that the teaching dimension in the class of threshold functions of $k$-valued logic in $n$ variables is $\Theta(\log^{n-2} k)$ for any fixed $n\ge 2$.

Reading the Stranger of Asylum Law: Legacies of Communication and Ethics

In this paper I argue the way in which the UK asylum system currently functions, fails to legally and discursively acknowledge the UK’s culpability and contribution to contexts that generate refugees via, for example, legacies of colonialism and engagement in neoliberal economic practices. I claim that these legacies fundamentally and detrimentally impact on, and delineate the relationship between, asylum claimant and immigration judge. Responding to these legacies and the concurrent interpersonal impact, I draw on the work of Iris Marion Young and Emmanuel Levinas in order to reframe the relationships between the interlocutors. Using an ethical framework, I focus on the benefits that engaging with, and bearing responsibility for the ‘other’ may have on the provision of justice for refugees. I rely in part on Iris Marion Young’s understanding of a communicative ethics based on ‘asymmetrical reciprocity’, which is indebted to Levinas’ conceptualisation of the other—the other as unknowable, and irreducible, and to whom we are obligated—in order to address the place of an ethics of responsibility (Levinas 2006; Hand 1996). Young’s work unpacks the relationship between locutionary positions; she relies on generosity towards the other through what she terms ‘the gift’ (Young 1997). The ‘gift’ is a relational concept—‘opening up to the other person is always a gift; the trust to communicate cannot await the other person’s promise to reciprocate’ (Young 1997, 351). The gift’s relationship to asymmetrical reciprocity requires each party to recognize and be open to the ‘irreducible points of view of the other’ and understand the ‘irreversibility’ of their subject positions (Young 1997, 351). I make this tentative turn to ethics as a way of repositioning the relationship of law to the politics of responsibility, in a bid to foster an ethical response to the other that reaches beyond the asylum court.

Master corner polyhedron: Vertices

We focus on the vertices of the master corner polyhedron (MCP), a fundamental object in the theory of integer linear programming. We introduce two combinatorial operations that transform vertices to their neighbors. This implies that each MCP can be defined by the initial vertices regarding these operations; we call them support vertices. We prove that the class of support vertices of all MCPs over a group is invariant under automorphisms of this group and describe MCP vertex bases. Among other results, we characterize its irreducible points, establish relations between a vertex and the nontrivial facets that pass through it, and prove that this polyhedron is of diameter 2.

Vertex Structure of Master Corner Polyhedra

Abstract We characterize irreducible points of master corner polyhedra, introduce two combinatorial operations that transform vertices to adjacent vertices, and describe the vertex structure and vertex bases of these polyhedra.

Gluing Seiberg-Witten monopoles

We establish a canonical gluing procedure for Seiberg-Witten monopoles on the two pieces of a closed, oriented four-manifoldX which is split along a 3-dimensional closed, oriented submanifold. We only assume that the (unperturbed) character variety is Kuranishi-smooth and the limiting maps are transversal | then we will be able to glue regular monopoles over the irreducible points of the character variety.

The law of the origin in the ontology of consciousness: (Descartes' third meditation)

The history of law is a history of finitude, which would be only one of the many histories of finitude, of the human condition or ontology. This irreducible point escapes those who invest all their efforts in understanding law through the scope of legitimacy how does the law come to calculate, decide, institute, pronounce and effect? By what right? On what foundation, origin, universalising pretext, does it so act? If we abandon this line of questioning, the pursuance ofwhich would only lead us through a gyre ofself-referential dilemmas circumventing the concept of 'origin', it becomes dear that it is precisely the role of the origin in its law-configuring mode that problematises what law can and does do, that is to say, what law is. But, even having isolated this theoretical agenda, there are no obvious signposts to navigate one's journey into this 'law-configuring origin'.

On retractable sets and the fixed point property

Call a subsetA of an ordered setP retractable tob e P↠ iff the map that mapsA tob and leaves all other points fixed is a retraction. We prove fixed point theorems for sets that contain a retractable set and also use this tool to study the fixed point property for products. The results in this paper show that three classical approaches to the fixed point property: irreducible points, cutsets and lexicographic sums can be viewed as special cases of the situation described above.

Über die irrednziblen punkte des eckenpolyeders

Considering a group knapsack problem we find some results on irreducible points being not extreme points of the corner polyhedron. The results are deduced from the fact that a feasible solution is irreducible iff it is not the arithmetic mean of two other easible solutions.

The role of unpaired forces in the lattice dynamics of covalent crystals

To study the lattice dynamics of covalent crystals, a model which, in addition to central (two-body) forces, involves unpaired forces of the type of D.C. Gazis, F. Herman, and R.F. Wallis [Phys. Rev. 119, 533 (1960)] has been developed. The model is used to calculate the phonon dispersion relations of diamond, silicon, and germanium at all the irreducible points of the first Brillouin zone and to calculate phonon density of states, lattice specific heats, and Debye characteristic temperatures. The R. Brout [Phys. Rev. 113, 43 (1954)] sum rule for ionic crystals as extended by H.B. Rosenstock [Phys. Rev. 129, 1959 (1963)]; H.B. Rosenstock and G. Blanken [Phys. Rev. 145, 546 (1966)] for diamond and zincblende crystals has also been verified by calculating the compressibilities of the above crystals. The model satisfies all the symmetry requirements of the perfect crystals. Results show reasonably good agreement with available experimental data.

The Lattice Dynamics of Quantum Crystals of F.C.C. 4He

AbstractThe lattice dynamics of solid helium in the f.c.c. phase is investigated using an unpaired elastic force model (EFM). The potential energy of the crystal is assumed to be made up of two parts: (1) the potential energy, giving rise to the central (pair‐wise) forces and 2. that one, giving rise to the unpaired forces. The model parameters are calculated using five experimental phonon frequencies. The frequency spectruy calculated at all the irreducible points of the first Brillouin zone is further used to compute the phonon density of states, lattice heat capacities, and Debye characteristic temperatures. The use of the model parameters is also made to predict the experimentally unavailable elastic constants in the f.c.c. phase. The theoretical results for the phonon frequencies along [100], [110], and [111] symmetry directions compare well with recent available experimental data.

Lattice Vibrations and Heat Capacities of Solid Neon and Xenon

The unpaired elastic force model (EFM) developed by Kushwaha and Kushwaha 1) has been extended to study the lattice dynamics of solid Neon (Ne) and Xenon (Xe). The application of the model has been made to calculate the phonon frequencies of Ne and Xe at all the irreducible points of the first Brillouin Zone. Use thereof has been made to calculate the lattice heat capacities and Debye characteristic temperatures in the temperature range 4–24 K and 4–100 K for Ne and Xe respectively. The calculated values of phonon frequencies along the three symmetry directions [100], [110], and [111], heat capacities and the Debye characteristic temperatures have been compared with the recent available experimental data. The merits and demerits of the model have been widely discussed.

The frequency spectra of solid neon and xenon

AbstractThe phonon frequencies of normal modes of vibration in solid neon and xenon are calculated at all the irreducible points of the first Brillouin zone with finer subdivisions (1000), using the unpaired‐elastic‐force model (EFM) recently developed. This is used to calculate the phonon densities of states. The calculated frequencies are compared in the highest symmetry directions [100], [110], and [111] with the recent available experimental data. It is observed that the theoretical results show a fairly good agreement with the neutron scattering measurements.

Frequency Spectra and Thermal Properties of Rare Gas Solids (Argon and Krypton)

AbstractThe unpaired elastic force model developed by the present authors is extended for studying the phonon frequencies of solid argon and krypton at all the irreducible points of the first Brillouin zone with finer subdivisions (1000). This is used to calculate the lattice heat capacities and Debye characteristic temperatures at different temperatures in the range 3 to 50 K. The comparison of theoretical values with the recently available experimental data reveals a fairly good agreement.

The description of the physical properties of condensed matter using irreducible tensors

Abstract A general framework for the description of the physical properties of condensed matter by irreducible tensors is presented. Irreducible tensors have been widely used in atomic and molecular physics but, surprisingly, less so in solid-state physics. In elasticity studies the strain and stress tensors are commonly decomposed into scalar (spherical) and deviatoric parts and more recently irreducible tensors have been introduced into discussion of non-linear optics and optical activity, but the approach is powerful and applicable to the analysis of the physical properties of condensed matter in general. The article aims to demonstrate this and to identify the kinds of argument about the properties of solids that can be best formulated in this way. The decomposition of a cartesian tensor into irreducible parts is considered for polar and axial tensors of rank n and the decompositions are given explicitly up to n = 4. Transformations of irreducible cartesian tensors into their spherical forms, and vice versa, are examined and the norm or magnitude is defined for reducible and irreducible tensors and applications are presented. Tensor index permutations are discussed with respect to their bearing on the decomposition of a tensor into irreducible points.