In this dissertation we discuss three problems. We first show the classical q-Stirling numbers of the second kind can be expressed more compactly as a pair of statistics on a subset of restricted growth words. We extend this enumerative result via a decomposition of a new poset which we call the Stirling poset of the second kind. The Stirling poset of the second kind supports an algebraic complex and a basis for integer homology is determined. A parallel enumerative, poset theoretic and homological study for the q-Stirling numbers of the first kind is done. We also give a bijective argument showing the (q, t)-Stirling numbers of the first and second kind are orthogonal. In the second part we give combinatorial proofs of q-Stirling identities via restricted growth words. This includes new proofs of the generating function of q-Stirling numbers of the second kind, the q-Vandermonde convolution for Stirling numbers and the q-Frobenius identity. A poset theoretic proof of Carlitz’s identity is also included. In the last part we discuss a new expression for q-binomial coefficients based on the weighting of certain 01-permutations via a new bistatistic related to the major index. We also show that the bistatistics between the inversion number and major index are equidistributed. We generalize this idea to q-multinomial coefficients evaluated at negative q values. An instance of the cyclic sieving phenomenon related to flags of unitary spaces is also studied.

abstract: The uncrossing partially ordered set $P_n$ is defined on the set of matchings on $2n$ points on a circle represented with wires. The order relation is $\tau'\leq \tau$ in $P_n$ if and only if $\tau'$ is obtained by resolving a crossing of $\tau$. %This partial order has been studied by Alman-Lian-Tran, Huang-Wen-Xie, Kenyon, and Lam. %The posets $P_n$ emerged from studies of circular planar electrical networks. Circular planar electrical networks are finite weighted undirected graphs embedded into a disk, with boundary vertices and interior vertices. By Curtis-Ingerman-Morrow and de Verdi\`ere-Gitler-Vertigan, the electrical networks can be encoded with response matrices. By Lam the space of response matrices for electrical networks has a cell structure, and this cell structure can be described by the uncrossing partial orders. %Lam proves that the posets can be identified with dual Bruhat order on affine permutations of type $(n,2n)$. Using this identification, Lam proves the poset $\hat{P}_n$, the uncrossing poset $P_n$ with a unique minimum element $\hat{0}$ adjoined, is Eulerian. This thesis consists of two sets of results: (1) flag enumeration in intervals in the uncrossing poset $P_n$ and (2) cyclic sieving phenomenon on the set $P_n$. I identify elements in $P_n$ with affine permutations of type $(0,2n)$. %This identification enables us to explicitly describe the elements in $P_n$ with the elements in $\mathcal{MP}_n$. Using this identification, I adapt a technique in Reading for finding recursions for the cd-indices of intervals in Bruhat order of Coxeter groups to the uncrossing poset $P_n$. As a result, I produce recursions for the cd-indices of intervals in the uncrossing poset $P_n$. I also obtain a recursion for the ab-indices of intervals in the poset $\hat{P}_n$, the poset $P_n$ with a unique minimum $\hat0$ adjoined. %We define an induced subposet $\mathcal{MP}_n$ of the affine permutations under Bruhat order. Reiner-Stanton-White defined the cyclic sieving phenomenon (CSP) associated to a finite cyclic group action on a finite set and a polynomial. Sagan observed the CSP on the set of non-crossing matchings with the $q$-Catalan polynomial. Bowling-Liang presented similar results on the set of $k$-crossing matchings for $1\leq k \leq 3$. In this dissertation, I focus on the set of all matchings on $[2n]:=\{1,2,\dots,2n\}$. I find the number of matchings fixed by $\frac{2\pi}{d}$ rotations for $d|2n$. I then find the polynomial $X_n(q)$ such that the set of matchings together with $X_n(q)$ and the cyclic group of order $2n$ exhibits the CSP. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2018

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<p>U radu je predložena modifikovana vatmetarska metoda za merenje snage gubitaka u toroidnim feritnim jezgrima koja je prilagođena osciloskopima male ulazne impedanse. Metoda je verifikovana na komercijalnim uzorcima od Mn-Zn i Ni-Zn feritnih materijala. Metoda je upotrebljena za merenje kompleksne permeabilnosti i gustine snage gubitaka dodatno obrađenih komercijalnih Mn-Zn feritnih prahova. Utvrđeno je da se dodatnim tehnološkim procesima (mlevenjem i prosejavanjem) početnog komercijanog praha mogu napraviti feritna jezgra manje gustine snage gubitaka i veće permeabilnosti.</p> / <p>The thesis proposes a modified Watt-meter method for measuring core loss of ferrite cores, which is adjusted to oscilloscopes with the small input impedance. The method is verified on comercial Mn-Zn and Ni-Zn ring cores. The method is used to measure the influence of starting powder sieving and milling on the core loss density and permeability of Mn-Zn ferrite. The experimental results and calculations show the significance of the additional milling and sieving process on magnetic properties of Mn-Zn ferrite in the frequency range from 0.1MHz to 10MHz. These processes increase the relative permeability about 3 times and decrease the core loss 4 times by milling of the starting powder.</p>

Για τον προσδιορισμό της πορομετρικής καμπύλης των γεωυφασμάτων διατίθενται σήμερα τρία πρότυπα (ASTM D6767, EN ISO 12956 και ASTM D4751) που θεωρούνται “διεθνούς” αποδοχής. Το πιο πρόσφατο από αυτά (ASTM D6767) εγκρίθηκε το 2002, ορίζει μέθοδο με βάση τη ροή σε τριχοειδή και αποτελεί το κύριο αντικείμενο της παρούσας διατριβής. Ελέγχθηκαν 52 μη υφασμένα γεωυφάσματα κατασκευασμένα από ίνες πολυπροπυλενίου τόσο κατά ASTM D6767 όσο και κατά EN ISO 12956 (υγρό κοσκίνισμα) και ASTM D4751 (ξηρό κοσκίνισμα). Τα αποτελέσματα που προέκυψαν συγκρίθηκαν τόσο μεταξύ τους όσο και με φυσικές ιδιότητες των γεωυφασμάτων, με τιμές μεγεθών που παρέχουν οι κατασκευαστές αυτών των προϊόντων και με τιμές μεγεθών που υπολογίζονται θεωρητικά. Τα μεγέθη πόρων και οι πορομετρικές καμπύλες που προκύπτουν εργαστηριακά με εφαρμογή κάθε μίας από τις τρεις μεθόδους είναι διαφορετικά. Αυτό οφείλεται στις διαφορετικές παραδοχές ή υποθέσεις κάθε μεθόδου αλλά και στις διαδικασίες που προβλέπει η κάθε μέθοδος. Ειδικότερα, οι δύο βασικές υποθέσεις του προτύπου ASTM D6767 αφορούν τη γωνία επαφής, θ, μεταξύ ρευστού και στερεού (τίθεται ίση με μηδέν) και τη μορφή της διατομής των πόρων των γεωυφασμάτων (κυλινδρική). Λόγω της δομής των μη υφασμένων γεωυφασμάτων οι δύο παραπάνω υποθέσεις δεν είναι δυνατόν να επαληθευθούν. Για τον λόγο αυτό στην εξίσωση προσδιορισμού των μεγεθών πόρων του προτύπου ASTM D6767 εισάγεται διορθωτικός συντελεστής. Από την επεξεργασία των αποτελεσμάτων της παρούσας διατριβής προέκυψε ότι ο συντελεστής αυτός πρέπει να έχει τιμή ίση με 1/3 (για τη συγκεκριμένη συσκευή που χρησιμοποιήθηκε και τις διαδικασίες που εφαρμόστηκαν για την εκτέλεση των δοκιμών) ώστε τα αποτελέσματα να προσεγγίζουν ικανοποιητικά αυτά της δοκιμής κατά EN ISO 12956. / Three internationally accepted standards (ASTM D6767, EN ISO 12956 and ASTM D4751) are available today for determing the pore size distribution of geotextiles. The most recently approved standard (2002) is ASTM D6767 which defines a method based on capillary flow. Laboratory testing according to this standard is the main subject of this thesis. Fifty two nonwoven geotextiles, made of polypropylene fibers, were tested according to the three standardized methods (ASTM D6767, EN ISO 12956 – wet sieving and ASTM D4751 – dry sieving). Comparisons were made between the results obtained from each standardized method as well as between measured pore sizes and geotextile physical properties, manufacturer provided pore sizes and values obtained theoretically. Different pore sizes and pore size distribution curves are obtained when different laboratory standard methods are applied. This is due to the different assumptions on which each method is based and also due to the procedures that each method specifies. The two main assumptions of the Standard ASTM D6767 concern the contact angle, θ, between liquid and solid (equal to zero) and the pore shapes of the geotextiles (cylindrical). Due to the structure of the nonwoven geotextiles the effect of these assumptions is different to quantify. Accordingly, the computation of pore sizes according standard ASTM D6767 is based on the introduction of a correction coefficient in the pertinent equation. The results obtained during this correction coefficient should have a value equal to 1/3 for the particular device used and the procedures applied. Use of this correction coefficient fields results that approximate very well the results obtained from wet sieving tests according to Standard EN ISO 12956.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniv. / Härtill 6 uppsatser.

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Fiber separation from these animal feeds could increase the protein and hence increase the value of the animal feed. The objective of the study was to evaluate the combination of sieving and air classification for fiber separation from soybean meal (SBM), cottonseed meal (CSM) and wheat middlings (WM). The effect of yields of lighter fractions on fiber separation from size fractions was also investigated. At low yields of lighter fraction (5%), the quantity of fiber product separated was 3.7, 1.3 and 4.8% by weight of SBM, CSM and WM respectively. At high yields of lighter fractions (15%), the quantity of fiber product separated was 8.9, 3.5 and 11% by weight of SBM, CSM and WM respectively. For CSM and SBM, the enhanced product contained 0.6 to 2.0% higher protein content than unprocessed feed. For WM, the enhanced product contained 0.2 to 0.7% higher protein content than unprocessed feed.