On the Exponential Bound of the Cutoff Resolvent

A simpler proof of a result of Burq [1] is presented.

Cramer-Rao bound analysis of location estimation in multi-hop wireless sensor networks

Location estimation is important for wireless sensor network (WSN) applications. In this paper we propose a Cramer-Rao Bound (CRB) based analytical approach for two centralized multi-hop localization algorithms to get insights into the error performance and its sensitivity to the distance measurement error, anchor node density and placement. The location estimation performance is compared with four distributed multi-hop localization algorithms by simulation to evaluate the efficiency of the proposed analytical approach. The numerical results demonstrate the complex tradeoff between the centralized and distributed localization algorithms on accuracy, complexity and communication overhead. Based on this analysis, an efficient and scalable performance evaluation tool can be designed for localization algorithms in large scale WSNs, where simulation-based evaluation approaches are impractical. © 2013 IEEE.

Pulse-to-pulse spectral evolution of breathing bound solitons in a mode-locked fiber laser

We make first direct observation of breathing bound solitons in mode-locked laser. We measure pulse-to-pulse spectrum evolution and reveal internal interactions between bound solitons in real-time. © OSA 2015.

An Improvement to the Achievement of the Griesmer Bound

We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper is to determine nq(k, d) for d = dk as nq(k, d) = gq(k, d) + 1 for q ≥ k with 3 ≤ k ≤ 8 except for (k, q) = (7, 7), (8, 8), (8, 9).

Note on an Improvement of the Griesmer Bound for q-ary Linear Codes

Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.

Polarization dynamics of bound state solitons in a carbon nanotubes mode locked erbium doped fiber laser

Optical solitons are important in the modern photonics. Passively mode locked erbium doped fiber lasers provide a neat platform to study soliton dynamics. Soliton interaction dynamics is important for various applications and has quite different manifestations, including e.g. such as bound state solitons [1], soliton rains [2]. Soliton interactions have been observed with different mode locking approaches such as figure-of-eight [3] and nonlinear polarization rotation [4]. Carbon nanotubes (CNT) have recently been widely applied as an efficient saturable absorber for passively mode locked fiber lasers. We have recently studied the polarization dynamics in a CNT mode locked vector soliton erbium doped fiber laser [5]. So far, the polarization dynamics of bound state solitons have yet to be investigated. In this report, we present a wide range of polarization dynamics of bound state solitons generated in a CNT mode locked erbium doped fiber laser. The fiber laser consists of ∼ 2 m highly doped erbium fiber (Liekki Er80-8/125) as the gain medium, an optical isolator to ensure unidirectional oscillation anda 980 nm laser diode is used to pump the gain through the 1550/980 nm wavelength division multiplexer. A fused 10:90 coupler is used to couple 10 % of the light out of the laser cavity and two in-line polarization controllers (NewPort) are used to control the birefringence of the cavity and polarization of the pump light respectively. The total cavity length is ∼ 7.8 m indicating a 25.7 MHz fundamental repetition rate. © 2013 IEEE.

New Upper Bound for the Edge Folkman Number Fe(3,5;13)

2000 Mathematics Subject Classification: 05C55.

Bound dissipative-pulse evolution in the all-normal dispersion fiber laser using a 45° tilted fiber grating

The formation and evolution of bound dissipative pulses in the all-normal dispersion Yb-fiber laser based on a novel 45° tilted fiber grating (TFG) are first investigated both numerically and experimentally. Based on the nonlinear polarization rotation technique, the TFG and two polarization controllers (PCs) are exploited for stable self-started passive mode locking. Numerical results show that the formation of bound-state pulses in the all-normal dispersion region is the progress of soliton shaping through the dispersive waves and follows the soliton energy quantization effect. Theoretical and experimental results demonstrate that the formation mechanism of bound-state pulses can be attributed to the high pump strength and effective filter bandwidth. The obtained bound-state dissipative pulses with quasi-rectangular spectral profile have fixed pulse separation as a function of pump power. © 2013 Astro Ltd.

A lower bound on the per soliton capacity of the nonlinear optical fibre channel

A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Multicolour nonlinearly bound chirped dissipative solitons

The dissipative soliton regime is one of the most advanced ways to generate high-energy femtosecond pulses in mode-locked lasers. On the other hand, the stimulated Raman scattering in a fibre laser may convert the excess energy out of the coherent dissipative soliton to a noisy Raman pulse, thus limiting its energy. Here we demonstrate that intracavity feedback provided by re-injection of a Raman pulse into the laser cavity leads to formation of a coherent Raman dissipative soliton. Together, a dissipative soliton and a Raman dissipative soliton (of the first and second orders) form a two (three)-colour stable complex with higher total energy and broader spectrum than those of the dissipative soliton alone. Numerous applications can benefit from this approach, including frequency comb spectroscopy, transmission lines, seeding femtosecond parametric amplifiers, enhancement cavities and multiphoton fluorescence microscopy.

FIU Medical Library Bound Journals

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Common Bound: The Small Groups of Methodism

The system of small groups John Wesley established to promote a proper life of discipleship in early Methodist converts was, in many respects, the strength of the Methodist movement. Those who responded to Wesley’s initial invitation to “flee the wrath to come” were organized into large gatherings called “societies,” which were then subdivided into smaller bands, class meetings, select societies, and penitent bands. The smaller groups gave Wesley the opportunity, through a system of appointed leaders, to keep track of the spiritual progress of every member in his movement, which grew to tens of thousands by the time of his death in 1791. As Methodism shifted from renewal movement to institutional church in the nineteenth century, however, growth slowed, and participation in such groups declined rapidly. By the early twentieth century, classes and bands were virtually extinct in every sector of Methodism save the African-American tradition. In recent years, scholars in various sectors of the Wesleyan tradition, particularly David Lowes Watson and Kevin Watson, have called for a recovery of these small groups for purposes of renewal in the church. There is no consensus, however, concerning what exactly contributed to the vitality of these groups during Wesley’s ministry.

Over the last century, sociological studies of group dynamics have revealed three common traits that are crucial to highly functioning groups: interdependence created by the existence of a common goal, interaction among group members that is “promotive” or cooperative in nature, and high levels of feedback associated with personal responsibility and individual accountability. All three of these were prevalent in the early Methodist groups. Interdependence existed around a shared goal, which for Wesley and the Methodists was holiness. That interdependence was cooperative in nature; individuals experienced the empowering grace of God as they each pursued the goal in the company of fellow pilgrims. Finally, the groups existed for purposes of feedback and accountability as individuals took responsibility both for themselves and others as they progressed together toward the goal of holy living. Wesley seemed to instinctively understand the essential nature of each of these characteristics in maintaining the vitality of the movement when he spoke of the importance of preserving the “doctrine, spirit and discipline” of early Methodism. Analysis of some of the present-day attempts to restore Wesley’s groups reveals frequent neglect to one or more of these three components. Perhaps most critical to recovering the vitality of the early Methodist groups will be reclaiming the goal of sanctification and coming to a consensus on what its pursuit means in the present day.

(Table 1) Comparison of diatom-bound and bulk sedimentary d15N values of ODP Holes 175-1082A and 175-1084A

The Matuyama Diatom Maximum (MDM) is a time of peak opal accumulation from 2.6 to ~2.0 Ma within the Benguela Current upwelling system that was initiated by increased influence of Southern Ocean water on the eastern South Atlantic. We measured opal, total organic carbon (TOC), and CaCO3 fluxes and C and N stable isotopes in sediments deposited from 2.4 to 1.95 Ma at Sites 1082 and 1084 to explore the biogeochemical dynamics within the Benguela region. The infusion of Southern Ocean water delivered dissolved nutrients and Southern Ocean flora and fauna, resulting in local opal accumulation increasing up to 8 g/cm**2/ky and the production of diatom mats. Some d15N measurements of diatom-bound organic matter indicate that the mats grew within the Benguela region. The bulk sediment d15N records are taken to reflect changes in the d15N of nitrate in the incoming water, where lower values at 2.4 Ma reflect less nitrate utilization in the Antarctic. A long-term increase in relative nitrate uptake in the Southern Ocean is evidenced by the gradual increase in d15N toward 1.9 Ma.

Stable isotope composition of diatom-bound organic matter

Oceanic nutrient cycling in the Southern Ocean is supposed to have an important impact on glacial-interglacial atmospheric CO2 changes and global climate. In order to characterize such nutrient cycling over the last two climatic cycles we investigated carbon and nitrogen isotopic ratios of diatom-bound organic matter (d13Cdiat and d15Ndiat, respectively) in two cores retrieved form the Atlantic and Indian sectors of the Antarctic Ocean. The two cores show the same isotopic patterns. The d13Cdiat values are depleted during glacial periods and enriched during interglacial periods, indicating lower productivity during cold times. The d15Ndiat values are enriched during glacial periods and depleted during interglacial periods, arguing for greater nitrate utilization during cold times. Taken at face value, this apparent contradiction leads to opposite conclusions on the role of the Southern Ocean biological pump on the atmospheric CO2 changes. However, the two sets of data can be reconciled by a "sea ice plus mixing rate scenario" that calls upon a balance between the effect of cutting off gas transfer at the ocean-atmosphere boundary and the effect of reducing vertical transport of nutrients through the pycnocline.