A system for measuring absolute frequencies of up to 4.25 THz using a Josephson point contact

A system for measuring the absolute frequency of a far-infrared (FIR) laser is described. Josephson point contacts have been utilized in the system as a frequency harmonic mixer connecting microwaves and optically pumped CH₃OH laser lines. The Josephson point contacts are capable of generating beat signals of 90 GHz microwaves and FIR waves of up to 4.25 THz. To measure the frequency of the beat signals from the Josephson junction with a frequency counter, tracking oscillators have been developed, which tracks the beat signals by phase locking and regenerate clean signals for frequency counting. It is shown that the absolute frequency can be measured to an accuracy of about 100 Hz by using the tracking oscillators.     

Mode-mode coupling theory of itinerant electron antiferromagnetism in superconducting state

It has been considered since the first discovery of a high-T(c) cuprate that an antiferromagnetic (AF) state and a superconducting (SC) state are separated in it. However, it is very intriguing that the coexistence of the AF and SC states has recently been observed in HgBa(2)Ca(4)Cu(5)O(12+) (Hg-1245). Moreover, it is very novel that this coexistence of these two states appears if the SC-transition temperature T(c) is higher than the AF-transition temperature T(N). The mode-mode coupling theory can provide a clear elucidation of this novel phenomenon. A key point of this theory is that the AF susceptibility consists of the random-phase-approximation (RPA) term and the mode-mode coupling one. The RPA term works to make a positive contribution to the emergence of the antiferromagnetic critical point (AF-CP). In contrast, the mode-mode coupling term works to make a negative contribution to the emergence of the AF-CP. However, the growth of the SC-gap function in the d(x(2)-y(2))-wave SC state works to suppress the negative contribution of the mode-mode coupling term to the emergence of the AF-CP. Moreover, the effect of SC fluctuations near the SC-transition temperature T(c) suppresses the mode-mode coupling term of the AF susceptibility that works to hinder the AF ordering. For these two reasons, there is a possibility that the d(x(2)-y(2))-wave SC state is likely to promote the emergence of the AF-CP. Namely, the appearance of the above-mentioned novel coexistence of the AF and SC states observed in Hg-1245 can be explained qualitatively on the basis of this idea.     

Moduli stacks and invariants of semistable objects on K3 surfaces

For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T. Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D. Joyce's work, we introduce the invariants counting semistable objects in D(X), and show that the invariants are independent of a choice of a stability condition.     

Normality of products of monotonically normal spaces with compact spaces

Let S be the class of all spaces, each of which is homeomorphic to a stationary subset of a regular uncountable cardinal (depending on the space). In this paper, we prove the following result: The product X×C of a monotonically normal space X and a compact space C is normal if and only if S×C is normal for each closed subspace S in X belonging to S. As a corollary, we obtain the following result: If the product of a monotonically normal space and a compact space is orthocompact, then it is normal.     

High performance "ionic liquid" chromatography

We firstly developed high performance liquid chromatography methods with "ionic liquids" as eluents (HPILC) and successfully demonstrated the analysis of various biopolymers including scarcely soluble highly polymerized cellulose by means of HPILC with highly polar ionic liquid.     

Bundling decisions in supply chains

Firms often sell products in bundles to extract consumer surplus. While most bundling decisions studied in the literature are geared to integrated firms, we examine a decentralized supply chain where the suppliers retain decision rights. Using a generic distribution of customers’ reservation price we establish equilibrium solutions for three different bundling scenarios in a supply chain, and generate interesting insights for distributions with specific forms. We find that (i) in supply chain bundling the retailer’s margin equals the margin of each independent supplier, and it equals the combined margin when the suppliers are in a coalition, (ii) when the suppliers form a coalition to bundle their products the bundling gain in the supply chain is higher and retail price is lower than when the retailer bundles the products, (iii) the supply chain has more to gain from bundling relative to an integrated firm, (iv) the first-best supply chain bundling remains viable over a larger set of parameter values than those in the case of the integrated firm, (v) supplier led bundling is preferable to separate sales over a wider range of parameter values than if the retailer led the bundling, and (vi) if the reservation prices are uniformly distributed bundling can be profitable when the variable costs are low and valuations of the products are not significantly different from one another. For normally distributed reservation prices, we show that the bundling set is larger and the bundling gain is higher than that for a uniform distribution.