This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.
Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve.
Equilibrium Constants of Liquid-liquid Distribution Reactions Introduction, and Part 1: Organophosphorus Extractants focuses on the numerical representations, formulas, reactions, and characteristics of equilibrium constants of organophosphorus extractants. The text underscores that only a number of papers focusing on equilibrium constants for distribution reactions involving metal complexes are published before 1947. The book also states that no equilibrium constants have been reported on several organophosphorus extractants although they are used in practical extraction work. The publication provides a list of extractants, ligands, and metal ions. These include distribution and dissociation of extractants; dimerization and aggregation of extractants; homogeneous equilibria of extractants with metal ions; extraction of metal ions with extractants as ligands; and reactions of extractants with diluents and other solvents. The manuscript also highlights reactions, temperature, and equilibrium constants. The book is a valuable source of data for readers interested in the equilibrium constants of organophosphorus extractants.
A Regency romance that proves not every match is made at the marriage mart—a sparkling series debut from the author of the Forever Brides books. After a disastrous, short-lived engagement and years of caring for her ailing grandmother, Phoebe Hallsmith is resigned to spinsterhood. But if she must be unmarried, far better to be of use than languishing at home, disappointing her parents. As an employee of the Everton Domestic Society of London, Phoebe accepts a position at the country home of an old friend and discovers an estate—and a lord of the manor—in a state of complete chaos. Losing himself in the bottle has done nothing to ease Markus Flammel’s grief over losing his wife. Not even his toddler daughter can bring him back from the brink. Now this fiery, strong-minded redhead has taken over his home, firing and hiring servants at will and arousing unexpected desire. As not one, but two, suitors suddenly vie for Phoebe’s hand, can Markus move past loss and fight for a future with the woman who has transformed his world? “If you love historical romance with a strong-willed heroine, this is a must-read! Fenichel’s outdone herself with a lush romantic story with honest, emotional depth, high stakes and humorous dialogue. I can’t wait for the next one in the series.”—N. N. Light’s Book Heaven “Much like the other books that I have read by A. S. Fenichel, the romance is complex yet lovely. I would recommend this book also for readers who love HEAs and overcoming large obstacles.”—JoJo’s Modern Life
Equilibrium Constants of Liquid-Liquid Distribution Reactions, Part III: Compound Forming Extractants, Solvating Solvents, and Inert Solvents focuses on the compilation of equilibrium constants of various compounds, such as acids, ions, salts, and aqueous solutions. The manuscript presents tables that show the distribution reactions of carboxylic and sulfonic acid extractants and their dimerization and other reactions in the organic phase and extraction reactions of metal ions from aqueous solutions. The book also states that the inorganic anions in these solutions are irrelevant, since they do not take part in the extraction reaction. The publication examines tables that illustrate the distribution of inorganic acids, salts, and complexes between aqueous solutions and solvents that have oxygen donor atoms. Tables that show the distribution of inorganic acids, salts, and complexes between aqueous solutions and inert solvents that do not have donor atoms and often utilized as inert diluents are also presented. The manuscript is a vital reference for readers and researchers interested in the equilibrium constants of compounds.
It is Spring, 1874, and twenty-year-old Sherlock Holmes is a lonely, mopey, friendless Oxford student. He attends classes and spends countless solitary hours conducting chemical experiments, reading, and playing his violin. Suddenly, his life changes because of a serendipitous moment on campus. While walking on the grounds of the university and practicing fencing moves with his foil, he encounters Victor Trevor and his sweetheart, Poppy Stamford, younger sister of the man who will one day introduce Sherlock to Dr. John Watson. Having just attended the final rowing contest of Eights Week, Victor and Poppy are also walking with her bull terrier. When the dog decides he doesn't like the looks of Sherlock, he sinks his teeth into Sherlock's ankle. This dog bite incident becomes a life-changing event for all of them. Through his new friendship with Victor Trevor and encouraged by Victor's father to use his genius for detective work, Sherlock discovers his uncanny abilities and a constellation of unfamiliar emotions as he and Poppy are thrust not only into a dangerous investigation into England's notorious baby-farming industry but into the perilous realm of young romance. Be an eyewitness to the emergence of how Sherlock became the man and the legend we know today….
The author of Tainted Bride returns to the Regency era with the heartwarming story of how two people turn their sadly-ever-after romance around. Elinor Burkenstock never believed in fairy tales. Sure, she's always been a fool for love—what woman isn't? But Elinor knows the difference between fiction and truth. Daydreams and reality. True love and false promises . . . Until the unthinkable happens, and Elinor's engagement is suddenly terminated and no one, least of all her fiancé, will tell her why. Sir Michael Rollins's war-hero days seem far behind him when, after one last hurrah before his wedding, he gets shot and his injuries leave him in dire shape. He wants nothing more than to marry Elinor, the woman of his wildest dreams. But Elinor's father forbids it . . . and soon Michael is faced with a desperate choice: Spare Elinor a life with a broken man or risk everything to win her heart—until death do they part?
An unexpected promise . . . an everlasting passion. An accomplished musician, Dorothea Flammel has refused more proposals than any London debutante; her only true love is her music. Dory’s shimmering talent and beauty have long been adored from afar by Thomas Wheel, an untitled gentleman who can only dream of asking for the hand of a nobleman’s daughter. But when her father, the insolvent Lord Flammel, arranges for Dory to marry a lecherous Earl in order to pay off a debt, she runs to Thomas—and proposes marriage to him. Eloping to Scotland saves Dory from a disastrous fate, but what is for her a mere marriage of convenience proves more passionate—and more complex—than either imagined as rumors, scandal, and buried emotions come to light. And when a vengeful challenge from a drunken and embittered Lord Flammel puts Thomas’s life on the line, will the fragile trust between husband and wife be enough to save them both?
A matchmaker breaks all the rules in this Regency romance from the author of A Lady’s Honor and the Forever Brides books—ebook includes a bonus prologue. Despite her disastrous London debut, Millicent Edgebrook has proven skilled at securing matches—for every young lady but herself. Resigned to spinsterhood, and eager to gain independence from her lovable but eccentric uncle, Millie joins the Everton Domestic Society. Her first assignment: find a bride for Preston Knowles, Duke of Middleton. How difficult can it be to secure a match for a handsome, eligible aristocrat? As difficult, it seems, as resisting her own attraction to the duke . . . Preston has promised himself not to be ruined by love. After being rebuffed by two perfectly respectable candidates, he’d rather remain happily single for the rest of his life . . . if only his mother would let him. Yet suddenly, he’s fantasizing about the lovely matchmaker she’s hired—the least suitable bride imaginable. Millie’s past is shrouded in scandal, and the Everton Society forbids relations between employees and clients. But even with so many obstacles against them, Preston longs to convince the woman he adores that love trumps rules every time. Praise for A Lady’s Honor—the first book in the Everton Domestic Society series “A lush romantic story with honest, emotional depth, high stakes and humorous dialogue.”—N. N. Light’s Book Heaven “Much like the other books that I have read by A. S. Fenichel, the romance is complex yet lovely. I would recommend this book also for readers who love HEAs and overcoming large obstacles.”—JoJo’s Modern Life
An American woman in London finds love among the ton, but a secret from her past threatens her happy future in this Regency romance series debut. Sailing to London, Sophia Braighton only hopes to escape certain ruin. But when she arrives, her Great Aunt Daphne has other plans for the American-born beauty. Determined to marry off her niece to a man of means, she propels Sophia into London society, not realizing the young woman’s trust in men is shattered. In fact, Sophia never expects to feel anything for a man. Then again, she never expects to find herself in the company of the dashing earl of Marlton . . . From the moment he sees Sophia, Daniel Fallon feels alive in a way he has not since his broken engagement. Though the vulnerable young woman shies from the passion burning between them, Daniel is determined to make her his bride. And when he learns of the painful secret she harbors, he is equally determined to take revenge on the man responsible. But will the quest destroy him—and his future with his beloved?
Not every match is made at the marriage mart… After a disastrous, short-lived engagement and years of caring for her ailing grandmother, Phoebe Hallsmith is resigned to spinsterhood. But if she must be unmarried, far better to be of use than languishing at home, disappointing her parents. As an employee of the Everton Domestic Society of London, Phoebe accepts a position at the country home of an old friend and discovers an estate—and a lord of the manor—in a state of complete chaos. Losing himself in the bottle has done nothing to ease Markus Flammel’s grief over losing his wife. Not even his toddler daughter can bring him back from the brink. Now this fiery, strong-minded redhead has taken over his home, firing and hiring servants at will and arousing unexpected desire. As not one, but two, suitors suddenly vie for Phoebe’s hand, can Markus move past loss and fight for a future with the woman who has transformed his world?
Lucky Linderman didn't ask for his life. He didn't ask his grandfather not to come home from the Vietnam War. He didn't ask for a father who never got over it. He didn't ask for a mother who keeps pretending their dysfunctional family is fine. And he didn't ask to be the target of Nader McMillan's relentless bullying, which has finally gone too far. But Lucky has a secret--one that helps him wade through the daily mundane torture of his life. In his dreams, Lucky escapes to the war-ridden jungles of Laos--the prison his grandfather couldn't escape--where Lucky can be a real man, an adventurer, and a hero. It's dangerous and wild, and it's a place where his life just might be worth living. But how long can Lucky keep hiding in his dreams before reality forces its way inside? Michael L. Printz Honor recipient A.S. King's smart, funny and boldly original writing shines in this powerful novel about learning to cope with the shrapnel life throws at you and taking a stand against it.
“That night he dreamt she ran towards him across a vast graveyard under a moonlit sky calling his name. He reached out to her but as fast as she ran she couldn’t close the distance. Then as if out of nowhere, she grasped his hand.” Set partly in late 1950’s London, Waiting for Walter follows the fortunes of two people over a forty-year time span, crisscrossing between countries. Days before his son’s marriage to an Asian girl, Martin is obsessed by a chance sighting of a familiar young woman on the other side of the street. Whilst wading through old love letters in his attic, a dried up ginkgo leaf falls to the floor and he is transported back to his romantic past to the girl who waited. In 1958, Martin, a Jewish boy, met Leni, a young German au pair, at The Moulin Rouge club in London. After a tempestuous start, they fell passionately in love. Secret plans to marry were made but in the aftermath of WW2 and the Holocaust, Martin’s father’s prejudice was immutable and Martin faced an impossible decision. Unable to stand up to his father and bridge the deep-rooted cultural divide, he makes a promise to each that he could not keep. Now in their sixties, and after years of sworn silence, Martin and Leni arrange to meet once more in Heidelberg. There, a single act of beauty and courage finally re-unites them in an unexpected farewell, leaving Martin with a heartbreaking dilemma... Waiting for Walter is a unique and powerfully moving love story with a historical setting and a strong sense of jeopardy. It will appeal to fans of Julian Barnes, David Nichols, and Colm Tóibín.
From the Booker Prize-winning author of Possession comes a wonderfully erudite novel in which enlightenment and sexuality, Elizabethan drama and contemporary comedy, intersect richly and unpredictably. "Large, complex, ambitious, humming with energy and ideas ... a remarkable achievement." —Iris Murdoch In Yorkshire, the Potter family are preparing to celebrate Elizabeth II’s arrival on the throne. Its three youngest members, however, are preoccupied with other matters. Stephanie has grown tired of their overbearing father and resolves to marry the local curate. Anxious teenager Marcus gains a new teacher and suffers increasingly disturbing visions. Then there is Frederica. On the brink of adulthood, a love affair with a young playwright may offer the freedom she desperately desires.
In this masterpiece about freedom, feminism, and destiny, Printz Honor author A.S. King tells the epic story of a girl coping with devastating loss at long last--a girl who has no idea that the future needs her, and that the present needs her even more. Graduating from high school is a time of limitless possibilities--but not for Glory, who has no plan for what's next. Her mother committed suicide when Glory was only four years old, and she's never stopped wondering if she will eventually go the same way...until a transformative night when she begins to experience an astonishing new power to see a person's infinite past and future. From ancient ancestors to many generations forward, Glory is bombarded with visions--and what she sees ahead of her is terrifying: A tyrannical new leader raises an army. Women's rights disappear. A violent second civil war breaks out. And young girls vanish daily, sold off or interned in camps. Glory makes it her mission to record everything she sees, hoping her notes will somehow make a difference. She may not see a future for herself, but she'll do anything to make sure this one doesn't come to pass.
Frederica Potter arrives at Cambridge University greedy for knowledge, sex and love. It isn’t long before she becomes infatuated with a mysterious and controlling poet. Back in Yorkshire, her sister Stephanie abandons academia and is confronted with the boredom and frustrations of motherhood. Meanwhile, their younger brother Marcus begins to recover from a nervous breakdown. Each sibling is desperate to shape their own future, but a horrifying event will soon change their lives forever.
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