Determinant formulas for class numbers in function fields

In this paper, by extending Kucera's idea to the function field case, we obtain several determinant formulas involving the real class number and the relative class number of any subfield of cyclotomic function fields. We also provide several examples using these determinant formulas.

     

Synthesis and characterization of new segmented polyurethanes with side‐chain,liquid‐crystalline chain extenders

Liquid‐crystalline, segmented polyurethanes with methoxy–biphenyl mesogens pendant on the chain extender were synthesized by the conventional prepolymer technique and esterification reaction. Two, side‐chain, liquid‐crystalline (SCLC) polyurethanes with mesogens having spacers of six and eight methylene units were prepared. The structures of the mesogenic units and SCLC polyurethanes were confirmed by Fourier transform infrared spectroscopy and ¹H NMR. Polymer properties were also examined by solubility tests, water uptakes, and inherent viscosity measurements. Differential scanning calorimetry studies indicated that the transition temperature of the isotropic to the liquid‐crystalline phase decreased with increasing spacer length. Wide‐angle X‐ray diffraction (WAXD) studies revealed the existence of liquid‐crystalline phases for both SCLC polyurethanes. Polarized optical microscopic investigations further confirmed the thermotropic liquid‐crystalline behaviors and nematic mesophases of both samples. Thermogravimetric analysis displayed better thermal stabilities for both SCLC polymers and indicated that the presence of mesogenic side chains may increase the thermal stability of segmented polyurethanes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 290–302, 2004     

Effects of poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] on the charge distributions of low‐density polyethylene/polystyrene blends

The effect of the triblock copolymer poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS) on the formation of the space charge of immiscible low‐density polyethylene (LDPE)/polystyrene (PS) blends was investigated. Blends of 70/30 (wt %) LDPE/PS were prepared through melt blending in an internal mixer at a blend temperature of 220 °C. The amount of charge that accumulated in the 70% LDPE/30% PS blends decreased when the SEBS content increased up to 10 wt %. For compatibilized and uncompatibilized blends, no significant change in the degree of crystallinity of LDPE in the blends was observed, and so the effect of crystallization on the space charge distribution could be excluded. Morphological observations showed that the addition of SEBS resulted in a domain size reduction of the dispersed PS phase and better interfacial adhesion between the LDPE and PS phases. The location of SEBS at a domain interface enabled charges to migrate from one phase to the other via the domain interface and, therefore, resulted in a significant decrease in the amount of space charge for the LDPE/PS blends with SEBS. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2813–2820, 2004     

A 0.25-/spl mu/m CMOS quad-band GSM RF transceiver using an efficient LO frequency plan

This paper describes a single-chip CMOS quad-band (850/900/1800/1900 MHz) RF transceiver for GSM/GPRS applications. It is the most important design issue to maximize resource sharing and reuse in designing the multiband transceivers. In particular, reducing the number of voltage-controlled oscillators (VCOs) required for local oscillator (LO) frequency generation is very important because the VCO and phase-locked loop (PLL) circuits occupy a relatively large area. We propose a quad-band GSM transceiver architecture that employs a direct conversion receiver and an offset PLL transmitter, which requires only one VCO/PLL to generate LO signals by using an efficient LO frequency plan. In the receive path, four separate LNAs are used for each band, and two down-conversion mixers are used, one for the low bands (850/900 MHz) and the other for the high bands (1800/1900 MHz). A receiver baseband circuit is shared for all four bands because all of their channel spaces are the same. In the transmit path, most of the building blocks of the offset PLL, including a TX VCO and IF filters, are integrated. The quad-band GSM transceiver that was implemented in 0.25-/spl mu/m CMOS technology has a size of 3.3/spl times/3.2 mm/sup 2/, including its pad area. From the experimental results, we found that the receiver provides a maximum noise figure of 2.9 dB and a minimum IIP3 of -13.2dBm for the EGSM 900 band. The transmitter shows an rms phase error of 1.4/spl deg/ and meets the GSM spectral mask specification. The prototype chip consumes 56 and 58 mA at 2.8 V in the RX and TX modes, respectively.     

Lossless subband coding system based on rounding transform

We propose a new rounding transform called the overlapping rounding transform (ORT). It is defined as a two-port input/two-port output FIR filtering system with a pair of rounding operations. The ORT is applied to develop lossless subband coding systems. The ORT approach has both a simpler representation and more possibilities for lossless subband implementation than the lifting scheme     

Dynamic Point Location in General Subdivisions

The dynamic planar point location problem is the task of maintaining a dynamic set S of n nonintersecting (except possibly at endpoints) line segments in the plane under the following operations:

• Locate (: point): Report the segment immediately above , i.e., the first segment intersected by an upward vertical ray starting at ;

• Insert (: segment): Add segment to the collection of segments;

• Delete (: segment): Remove segment from the collection of segments.

We present a solution which requires space O(n) and has query and insertion time O(log n log log n) and deletion time O(log²n). The bounds for insertions and deletions are amortized. A query time below O(log²n) was previously only known for monotone subdivisions and subdivisions consisting of horizontal segments and required nonlinear space.     

Advantages of CDMA and spread spectrum techniques over FDMA andTDMA in cellular mobile radio applications

A unified theoretical method for the calculation of the radio capacity of multiple-access schemes such as FDMA (frequency-division multiple access), TDMA (time-division multiple access), CDMA (code-division multiple access) and SSMA (spread-spectrum multiple access) in noncellular and cellular mobile radio systems is presented for AWGN (additive white Gaussian noise) channels. The theoretical equivalence of all the considered multiple-access schemes is found. In a fading multipath environment, which is typical for mobile radio applications, there are significant differences between these multiple-access schemes. These differences are discussed in an illustrative manner revealing several advantages of CDMA and SSMA over FDMA and TDMA. Novel transmission and reception schemes called coherent multiple transmission and coherent multiple reception are briefly presented     

Stability control of the electrooptic effect with new maleimide copolymers containing photoreactive tricyanopyrrolidene‐based chromophores

New photocrosslinkable maleimide copolymers have been synthesized by the attachment of a tricyanopyrrolidene‐based chromophore. The 2‐(3‐cyano‐4‐(2‐{4‐[hexyl‐(6‐hydroxy‐hexyl)‐amino]‐phenyl}‐vinyl)‐5‐oxo‐1‐{4‐[4‐(3‐oxo‐3‐phenyl‐propenyl)‐ phenoxy]‐butyl}‐1,5‐dihydro‐pyrrol‐2‐ylidene)‐malononitrile chromophore exhibits nonlinear optical activity and contains a chalcone moiety that is sensitive to UV light (λ = 330–360 nm) for crosslink formation. The maleimide monomers have also been functionalized with chalcone moieties. The resultant copolymers exhibit great processability, and one of them shows a maximum electrooptic coefficient of 90 pm/V at 1300 nm. We could control the thermal stability of the electrooptic coefficient with the newly synthesized photoreactive copolymers successfully. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 531–542, 2007     

Cellulose dimethylphenylcarbamate-bonded carbon-clad zirconia for chiral separation in high performance liquid chromatography.

Porous zirconia particles are very robust material and have received considerable attention as a stationary phase support for HPLC. We prepared cellulose dimethylphenylcarbamate-bonded carbon-clad zirconia (CDMPCCZ) as a chiral stationary phase (CSP) for separation of enantiomers of a set of 14 racemic compounds in normal phase (NP) and reversed-phase (RP) liquid chromatography. Retention and enantioselectivity on CDMPCCZ were compared to those on CDMPC-coated zirconia (CDMPCZ) to see how the change in immobilization method of the chiral selector affects the retention and chiral selectivity. In NPLC, retention was longer and the number of resolved racemates was smaller on CDMPCCZ than on CDMPCZ. However, chiral selectivity factors for some resolved racemates were better on CDMPCCZ than on CDMPCZ. The longer retention on CDMPCCZ is likely due to strong, non-chiral discriminating interactions with the carbon layer on CDMPCZ. In RPLC only two racemates were resolved on CDMPCCZ, but retention times were shorter than, and resolutions were comparable to, those in NPLC, indicating a potential for improving chromatographic performance of the CDMPCCZ column in RPLC with optimized column preparation and separation conditions.