Quadratic operator equations and periodic operator continued fractions

AbstractConditions are given that assure convergence of an operator-valued periodic continued fraction of period two. These results and techniques are applied to get a solution of the quadratic operator equation in a complex Hilbert space. Special attention is then given to the important case of the quadratic matrix equation connected with the steady-state solution of the matrix Riccati equation from control theory. It is shown that a modification of the traditional matrix power approximation technique leads to a new, efficient and highly simplified method of approximating the unique nonnegative definite solution that exists in many important special cases

Nurturing the talent pipeline for an emerging global workforce

Passion. IMSA’s ability to produce thinkers and problem solvers doesn’t just breed pragmatists who know what it takes to be successful – it also gives students the chance to discover their passion. The more they try and the more they experience, the more they discover what they love. The chance to pursue passion means graduates have a greater sense of vision – and a greater chance of realizing their true potential. IMSA teaches students to be global citizens in a diverse world. IMSA embraces diverse perspectives enriching understanding and the knowledge, attitudes, and skills required to function as multicultural citizens in a global world. The false perception that IMSA is just a school for smart kids might blind people from seeing what truly makes IMSA special. There are plenty of places to be smart – IMSA shares in the responsibility to enable students to be successful in the emerging future of a global workforce

Estimating Natal Origins of Migratory Juvenile Northern Goshawks Using Stable Hydrogen Isotopes

From 2004 to 2007, we collected hatch-year feathers from 44 juvenile Northern Goshawks (Accipiter gentilis) captured at our Rocky Mountain Front banding station near Lincoln, Montana. Due to the relative scarcity and secretive nature of goshawks, little is understood about their migration patterns or the geographic origins of birds encountered at research sites. Most studies suggest goshawks are partial migrants, often moving <100km, but select band returns and radio and satellite telemetry have shown some individuals occasionally travel thousands of kilometers. We performed a stable hydrogen isotope analysis on the feathers we collected from young goshawks to determine their predicted natal origin. We found that 68% of goshawks had predicted natal origins relatively close to our capture site, 25% from areas in northwestern Canada and eastern Alaska, and 7% somewhere significantly south or east of our capture site. We did not find any significant patterns with sex and passage date or latitudinal origin, nor did we find a meaningful relationship between latitudinal origin and passage date. Our findings support the current understandings of goshawk migration, with a majority of individuals traveling short distances from their natal grounds and a few outliers traveling great distances, not always in a southerly direction

A segmented and clawed male foreleg in a newly described genus and species of eumaeine butterfly (Lepidoptera: Lycaenidae)

Grishinata Robbins and Busby, new genus (Lepidoptera: Lycaenidae: Eumaeini), possesses a five-segmented foretarsus with a clawed pretarsus, a trait that differentiates it from all eumaeine genera except Theclopsis Godman and Salvin. Grishinata penny Busby, Hall, and Robbins, new species, differs from all species of Theclopsis (and most Eumaeini) in lacking male secondary sexual organs on the wings or in the abdomen. It is recorded from the eastern slope of the Andes in Ecuador and Peru. We cannot place Grishinata penny in an existing Eumaeini genus based upon its wing pattern, male foreleg structure, lack of male second­ary sexual organs, and male genitalic morphology. We propose names for the genus and species to document its leg morphology and to provide a name for a genome sequencing project, which will allow us to place the genus in the eumaeine Linnaean hierarchy. There are two morphological types of male forelegs in the lepidopteran butterfly family Lycaenidae, each of which is functionally and structurally different from male forelegs in other diurnal butterfly families. The first male foreleg type is superficially similar to that of Nymphalidae and Riodinidae in that the tarsus is unsegmented, lacks a pretarsus, and is not used to groom the antennae (Robbins 1988, 1990). It differs functionally from these families in that it is used for walking. It differs morphologically in that it possesses tarsal alpha and beta trichoid sensilla (terminology from Chun and Schoonhoven 1973), which are lacking in Nymphalidae and Riodinidae with few exceptions (Robbins 1988). This male foreleg type occurs in more than 98% of lycaenid species (Mattoni and Fiedler 1991). The second lycaenid male foreleg type is superficially similar to that of Hesperiidae, Papilionidae, and Pieridae in that the foretarsus is segmented with a clawed pretarsus. It differs functionally from these families in that it is not used to groom the antennae (Jander 1966; Robbins 1990). It differs morphologically in that it lacks the tibial epiphysis of Hesperiidae and Papilionidae or the vestigial remnant of an epiphysis that occurs in some Pieridae (Robbins 1990). Within Eumaeini, this male foreleg type is restricted to some species of Theclopsis Godman and Salvin, 1887 (Godman and Salvin 1887; Robbins 2004). We discovered a species (Fig. 1) belonging to the Eumaeini with a male foreleg that has a clawed pretarsus and a five-segmented tarsus (Fig. 2), but the male genitalia, secondary sexual characters, and wing pattern (Fig. 1, 3) are dissimilar from those of Theclopsis. The males lack secondary sexual organs on the wings or in the abdomen (Fig. 1, 3), which is highly unusual in Eumaeini (Valencia-Montoya et al. 2021). The male genitalia (Fig. 3) lack structures that would be useful in determining its closest phylogenetic relatives. More generally, we find no clear-cut morphological evidence to place this species in an available eumaeine genus. The purpose of this paper is to propose new generic and specific names for this newly discovered taxon. One reason is that we need a name to document its unusual leg morphology. Another is that we are currently sequencing its genome for a phylogenetic project. Phylogenetic analysis of the sequence data will allow us to place the genus in the eumaeine Linnaean hierarchy. We predict that it will show, in accord with the findings of Mattoni and Fiedler (1991), that its male foreleg with a clawed pretarsus and five-segmented tarsus evolved from a tarsus that was fused without a pretarsus

Unlocking the potential of geothermal energy in the UK

This report is intended to provide technical information that complement the BGS Science Briefing Note: Deep impact: Unlocking the potential of geothermal energy for affordable low-carbon heating in the UK [1]. It gives a general overview of the deep geothermal opportunities that exist in the UK (although regional geothermal potential is not discussed here) as well as of financial, policy and regulatory actions that are needed to support the effective development and exploitation of deep geothermal resources in the UK. The recommendations are applicable to the UK government and its departments as well as to devolved administrations in Scotland, Northern Ireland and Wales, and devolved policy areas, such as heat policy and planning, in the respective nations. Following the introduction, the report is organised in three sections. In Section 1, details are given of the UK’s deep geothermal resources and how and where they could be utilised. Section 2 focuses on the experiences of continental Europe and the policies that have enabled the growth of a geothermal industry. Section 3 considers key policies and regulatory actions identified as necessary to drive the development of the UK geothermal sector from its current status of infancy to a mature technology that is universally recognised and utilised by a wide range of stakeholders, end-users and supported by investors

Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector

We report on the optical response of a suspended-mass detuned resonant sideband extraction (RSE) interferometer with power recycling. The purpose of the detuned RSE configuration is to manipulate and optimize the optical response of the interferometer to differential displacements (induced by gravitational waves) as a function of frequency, independently of other parameters of the interferometer. The design of our interferometer results in an optical gain with two peaks: an RSE optical resonance at around 4 kHz and a radiation pressure induced optical spring at around 41 Hz. We have developed a reliable procedure for acquiring lock and establishing the desired optical configuration. In this configuration, we have measured the optical response to differential displacement and found good agreement with predictions at both resonances and all other relevant frequencies. These results build confidence in both the theory and practical implementation of the more complex optical configuration being planned for Advanced LIGO

Finishing Steers in a Deep-bedded Hoop Barn and a Conventional Feedlot: Effects on Behavior and Temperament during Summer in Iowa

As the Iowa beef industry invests in environmental management, there has been increasing interest in systems where runoff is minimized. A possible housing option used previously for pigs and sheep to help mitigate some of these environmental concerns are hoops. The objective of this study was to compare steer behavior and temperament between two treatments; hoop building (HP; n=3; 4.65m 2 / steer) vs. conventional feedlot (FD; n=3; 14.7m 2 / steer) during the summer months. A total of 240 crossbred Bos taurus steers were used. Steers were ear tagged, implanted, and weighed (445 ± 31.7 kg) on arrival and allotted to balance weight and breed. Behavioral data were collected using a 10 min scan sampling technique using live observation by two experienced observers from 0700 h to 1600 h on d 34, 56 and 91 of the trial. Two behaviors (head in bunk and head in waterer) and three postures (lying, walking and standing) were recorded. One day postbehavior collection, steers were moved through a squeeze chute for subjective temperament scoring. Scores ranged from 1 (exits chute calmly) to 6 (very aggressive, charges handlers). There were no (P = 0.22) differences for head in bunk behavior between treatments, however there was a difference (P = 0.02) for drinking, with HP steers spending more time at the waterer than FD steers. Lying incidence was greater (P = 0.004) for HP vs. FD steers. Fewer (P \u3c 0.05) HP steers exhibited walking or standing behavior compared to their FD counterparts. Temperament scores were not different between treatments (P = 0.13) but day and day*treatment (P \u3c 0.001) were sources of variation for temperament measures. In conclusion, overall time budget differences were observed with HP steers being less active but spending more time engaged in drinking related behaviors. Temperament scores increased during the trial but did not differ between the two housing treatments. Therefore, housing steers in a hoop barn does not result in detrimental alterations in either behavior or temperament when compared to steers in a conventional feedlot

Translation of a minigene in the 5′ leader sequence of the enterohaemorrhagic Escherichia coli LEE1 transcription unit affects expression of the neighbouring downstream gene

The 5′ end of the major RNA transcript of the LEE1 operon of enterohaemorrhagic Escherichia coli contains ~170 bases before the AUG translation start codon of the first recognized gene, ler. This unusually long leader sequence carries three potential alternative AUG start codons. Using a lac fusion expression vector, we confirmed that the ler gene AUG is functional for translation initiation, and we checked for translation initiation at the three alternative AUG codons. Whereas two of the alternative AUG codons appear incompetent for translation initiation, we detected strong initiation at the third AUG, which is followed by one AAA codon and a UAG stop codon. The location of this very short two-codon open reading frame with respect to the ler translation start appears to be critical. Hence mutations that destroy the UAG stop codon, or short deletions between the UAG stop codon and the ler translation initiation region, result in big effects on ler expression. In the context of the full-length LEE1 operon leader sequence, translation of this very short two-codon open reading frame is necessary for optimal expression of the ler gene and for the subsequent interactions of enterohaemorrhagic Escherichia coli with host target cells