Dissecting a brick into bars

Consider the set of all lengths of sides of an N-dimensional parallelepiped. If this set has no more than k elements, the parallelepiped will be called a bar (the definition of a bar depends on k). We prove that a parallelepiped can be dissected into a finite number of bars if and only if the lengths of its sides span a linear space of dimension at most k over \mathbb Q{{\mathbb Q}} . This extends and generalizes a well-known theorem of Max Dehn about the splitting of rectangles into squares. Several other results about dissections of parallelepipeds are obtained.     

Interferometric ultrafast SOA-based optical switches: From devices to applications

All-optical switches are fundamental building blocks for future, high-speed optical networks that utilize optical time division multiplexing (OTDM) techniques to achieve single channel data rates exceeding 100 Gb/s. Interferometric optical switches using semiconductor optical amplifier (SOA) non-linearities perform efficient optical switching with < 500 fJ of control energy and are approaching optical sampling bandwidths of nearly 1 THz. In this paper, we review work underway at Princeton University to characterize and demonstrate these optical switches as processing elements in practical networks and systems. Three interferometric optical switch geometries are presented and characterized. We discuss limitations on the minimum temporal width of the switching window and prospects for integrating the devices. Using these optical switches as demultiplexers, we demonstrate two 100-Gb/s testbeds for photonic packet switching. In addition to the optical networking applications, we have explored simultaneous wavelength conversion and pulse width management. We have also designed high bandwidth sampling systems using SOA-based optical switches as analog optical sampling gates capable of analyzing optical waveforms with bandwidths exceeding 100 GHz. We believe these devices represent a versatile approach to all-optical processing as a variety of applications can be performed without significantly changing the device architecture.     

Development of special optical fibers for evanescent-wave chemical sensing

The paper summarizes results achieved in the Institute of Radio Engineering and Electronics in the field of investigation and fabrication of novel fiber-optic structures for evanescent-wave chemical sensing. Several approaches for increasing the evanescent-wave sensitivity of multimode silica optical fibers to gaseous and liquid chemicals are shown. These approaches make use of the decrease of the core diameter in sectorial and capillary sectorial fibers, modification of trajectories of optical rays in the cores of inverted-graded-index fibers, tailoring of the refractive index of porous layers applied on silica cores, an output mode filter preventing the detection of rays propagating at low axial angles or fibers bent in single or multiple turns. Presented at the 1st Czech-Chinese Workshop “Advanced Materials for Optoelectronics”, Prague, Czech Republic, June 13–17, 1998. This work was supported by the Grant Agency of the Czech Republic (projects No. 102/96/0939 and No. 102/98/1358) and by joint project No. 4104 of AS CR and CNRS, France.     

A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras

Let be a toroidal Lie algebra corresponding to a semisimple Lie algebra We describe all Borel subalgebras of which contain the Cartan subalgebra where is a fixed Cartan subalgebra of We show that each such Borel subalgebra determines a parabolic decomposition where is a proper toroidal subalgebra of and Our first main result is that, for any weight which does not vanish on , an arbitrary subquotient of the Verma module is induced from its submodule of invariant vectors. This reduces the study of subquotients of to the study of subquotients of Verma modules over . We then introduce categories and and their respective blocks and corresponding to a central charge which is nonzero on . Our second main result is that the functors of induction and invariants are mutually inverse equivalences of the category and the full subcategory of whose objects are generated by their invariants.     

Assembly of Tetrazolylfuroxan Organic Salts: Multipurpose Green Energetic Materials with High Enthalpies of Formation and Excellent Detonation Performance

A series of highly energetic organic salts comprising a tetrazolylfuroxan anion, explosophoric azido or azo functionalities, and nitrogen-rich cations were synthesized by simple, efficient, and scalable chemical routes. These energetic materials were fully characterized by IR and multinuclear NMR (¹H, ¹³C, ¹⁴N, ¹⁵N) spectroscopy, elemental analysis, and differential scanning calorimetry (DSC). Additionally, the structure of an energetic salt consisting of an azidotetrazolylfuroxan anion and a 3,6,7-triamino-7H-[1,2,4]triazolo[4,3-b][1,2,4]triazolium cation was confirmed by single-crystal X-ray diffraction. The synthesized compounds exhibit good experimental densities (1.57–1.71 g cm⁻³), very high enthalpies of formation (818–1363 kJ mol⁻¹), and, as a result, excellent detonation performance (detonation velocities 7.54–8.26 kms⁻¹ and detonation pressures 23.4–29.3 GPa). Most of the synthesized energetic salts have moderate sensitivity toward impact and friction, which makes them promising candidates for a variety of energetic applications. At the same time, three compounds have impact sensitivity on the primary explosives level (1.5–2.7 J). These results along with high detonation parameters and high nitrogen contents (66.0–70.2 %) indicate that these three compounds may serve as potential environmentally friendly alternatives to lead-based primary explosives.     

Ten-membered rings as key interaction motifs in folding of desmuramyl di-, tri-, and tetrapeptides

Structural Chemistry - Muropeptides are fragments of polymeric peptidoglycan, unique constituent of bacterial cell walls, acting as immunostimulators (adjuvants). The smallest biologically active...     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance-dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short-range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O⋅⋅⋅C=O interactions.