Approximation properties of β-expansions II, Ergodic Theory and Dynamical Systems, 38 (2018), no. Mathe), Ergodic Theory and Dynamical Systems, 39 (2019), no. Inhomogeneous self-similar sets with overlaps (with J. Steiner), Bulletin of the London Mathematical Society, 49 (2017): 58–-70.ġ5. On the regularity of the generalised golden ratio function (with W. Unique expansions and intersections of Cantor sets (with D. On periodic representations in non-Pisot bases (with Z. Kong), Transactions of the American Mathematical Society, 371 (2019), no. Entropy, Topological transitivity, and Dimensional properties of unique q-expansions (with R. An analogue of Khintchine’s theorem for self-conformal sets, Math. Yu), Computational Methods and Function theory, 18 (2018), no. Root sets of polynomials and power series with finite choices of coefficients (with H. Digit frequencies and self-affine sets with non-empty interior, Ergodic Theory Dynam. Bifurcation sets arising from non-integer base expansions (with P. Kong), Mathematical Proceedings of the Cambridge Philosophical Society, 167(1), 171-192.Ģ3. Numbers with simply normal β-expansions (with D. Exceptional digit frequencies and expansions in non-integer bases, Monatsh Math 190, 1–31 (2019).Ģ4. Maximising Bernoulli measures and dimension gaps for countable branched systems (with N. A General Mass Transference Principle (with D. Infinitely generated self-similar sets with positive Lebesgue measure and empty interior (with N. On the complexity of the set of codings for self-similar sets and a variation on the construction of Champernowne (with D. Overlapping iterated function systems from the perspective of Metric Number Theory, 78 pages, Memoirs of the American Mathematical Society (to appear).Ģ9. Two bifurcation sets arising from the beta transformation with a hole at 0 (with D. Equidistribution and the shrinking target problem for sequences of polynomials, Journal of Number Theory, 215 (2020), 1-19.ģ1. Iterated function systems with super-exponentially close cylinders, Adv. Quantitative recurrence properties for self-conformal sets (with M. On the pair correlations of powers of real numbers (with C. Equidistribution results for self-similar measures, 17 pages, IMRN (to appear).ģ5. Iterated function systems with super-exponentially close cylinders II, Proc. Analogues of Khintchine’s theorem for random attractors, (with S. Gap statistics and higher correlations for geometric progressions modulo one, (with C. New dimension bounds for αβ sets, Journal of Number Theory 228 (2021), 59–72.ģ9. Intrinsic Diophantine Approximation for overlapping iterated function systems, 31 pages, Math. Metric results for numbers with multiple q-expansions, (with Y. Algom and Pablo Shmerkin) 14 pages, Advances in Mathematics (to appear).Ĥ2. On normal numbers and self-similar measures, (with A. Approximating elements of the middle third Cantor set with dyadic rationals, Israel J. Yu) 5 pages, Indagationes Mathematicae (to appear).Ĥ4. A note on dyadic approximation in Cantor’s set, (with D. Recurrence rates for shifts of finite type, (with D. Quantitative recurrence and the shrinking target problem for overlapping iterated function systems, (with H. Spectral gaps and Fourier dimension for self-conformal sets with overlaps, (with T.
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When a man says, "I don't want a relationship," what he means is, "I don't want a relationship." Or, specifically, "I don't want a relationship with you." It does not mean, "I'm broken and you can fix me." Or, "If the sex is really great I will commit to you. Listen to what a man is saying and take a rejection at face value. Don't confuse a sexual connection for the beginning of a relationship. My thing is that i dont have a problem being exclusive it, But her making we are not a couple really irritated me and makes me question her intentions. Here the partners are committed to staying in the relationship (for the children, because of a religious conviction, or because there are no alternatives. If, however, you're looking for something more, then please don't get involved with a player. Pedophilia (alternatively spelt paedophilia) is a psychiatric disorder in which an adult or older adolescent experiences a primary or exclusive sexual attraction to prepubescent children.: vii Although girls typically begin the process of puberty at age 10 or 11, and boys at age 11 or 12, criteria for pedophilia extend the cut-off point for prepubescence to age 13. Most of these men are upfront from the start that they're just seeking hook-ups and are not in the market for a relationship. They enjoy sleeping with lots of women and have no intention of settling down. Maybe the do want a traditional relationship but its just early and they simply want to enjoy safer sex. If half the men each take two wives, the other half must remain wifeless. Exclusivity should not be confused with long term commitment. Or perhaps he openly admits that he is "too selfish" and "loves his lifestyle". Given a roughly 50-50 sex ratio, the highest proportion of men in polygynous marriage in any society is 50. That isn't quite as workable, unless he's been in some intense therapy There is no need to rush through this important final stage, and every reason to go slowly. Perhaps his heart was broken as a very young man and he has feared commitment ever since. Being sexually exclusive with someone means having a monogamous relationship with them, where both parties agree to only be intimate with each other. Perhaps he has been too consumed by his career, but feels ready now to focus on love. First published: 30 June 2020 Citations: 3 Sections PDF Tools Share Abstract Sexual infidelity is widespread, but it is also widely condemned, yet relatively little philosophical work has been done on what makes it wrong and how wrong it is. Our teams can take your old furniture away on a like for like basis - we are charged by our recycling company as shown in the tariff below. 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Know your real strengths, weaknesses, abilities, and talents. Life Path Number: the path(route) that should be taken to excel in life.Īttitude Number: the attitude towards Life needed to be successful. Power Number: the strengths of a character.īirthday Number: it is about the first impression of a character. Personality Number: the characteristics (features) of a character. Soul’s Urge: it is related to one’s inner desires. There are six important numbers in the numerological chart(numerological portrait), they are: Life path describes the best way in which a person can live his life to the fullest. This is how numerology love prediction rolls too. It is calculated by adding all the single-digit numbers from the birthday – date, month and year into a single digit. While talking about the significance of other numbers, the life path number is considered the most important. From these six digits, three are calculated on the basis of date of birth, and the other three are calculated on the basis of numbers pulled from the letters of a person’s name. It is the personalized guide by which a person can find out his strengths, weaknesses, and what can it lead to.Īs in Astrology, you can personality portrait is formed on the basis of your date of birth, time and place in Numerology, it is a bit easier here, it is calculated on the basis of just six numerals in the numerological chart. Numerology Portrait is something similar to an astrological natal chart. Similarly, in Tarot, each card is numbered, and it holds its own significance.įind what Stores in your life based on Planets. Thus this idea of assigning numerical values to the letters came to be known as Pythagoras Number System.Īlso, the significance of numbers can be seen in various religious books throughout the world, such as 888 represents Jesus, 666 is associated with beast. He believed that the numbers from 1 to 9 are very significant, and everything in life can be translated into this form. He went to Egypt to study Chaldean Numerology for 22 years. Although much of his life remained a mystery, his passion for numbers was well documented and had shreds of evidence for them. He was a great mathematician and a philosopher. He could find out the relativity of numbers to everything in life. Numbers were more than a mystery for him. While some records were from Ancient Egypt, China, Rome, Japan and Greece, it was the Greek Philosopher Pythagoras who came to be known as the father of Numerology. Numerical ideas were in existence before 1907, but numerology wasn’t discovered until then. Gigi has similarly requested privacy, with a representative for the model telling E! News ‘Gigi is solely focused on the best for Khai. ‘I am hopeful though for healing for all involved with the harsh words shared and more importantly I remain vigilant to protect Khai and give her the privacy she deserves.’ ‘This was and still should be a private matter but it seems for now there is a divisiveness and despite my efforts to restore us to a peaceful family environment that will allow for me to co-parent my daughter in a manner which she deserves, this has been “leaked” to the press,’ he continued. In an effort to protect that space for her I agreed not to contest claims arising from an argument I had with a family member of my partners who entered our home while my partner was away several weeks ago. ‘A place where private family matters aren’t thrown on the world stage for all to poke and pick apart. ‘As you all know I am a private person and I very much want to create a safe and private space for my daughter to grow up in,’ he wrote. Zayn later posted a further statement on Twitter elaborating on the argument that led to this fallout. ‘I adamantly deny striking Yolanda Hadid and for the sake of my daughter I decline to give any further details and I hope that Yolanda will reconsider her false allegations and move towards healing these family issues in private,’ he said. It’s the story that continues to take over our timelines, with Zayn previously releasing a statement denying TMZ’s claim that he ‘struck’ Yolanda. According to TMZ, while official documents state that Zayn pleaded guilty to one count of harassment, court officials state that he actually pleaded no contest. Now, it's been reported that Zayn was charged with four criminal offences of harassment against Yolanda and Gigi. Why? Because after TMZ reported that Yolanda had accused Zayn of assaulting her, the gossip website later revealed that Zayn and Gigi Hadid have split. This morning, Zayn Malik and Yolanda Hadid were trending on Google. “.skilled abacus users perform rapid and precise mental arithmetic by manipulating a mental representation of an abacus, which is based on visual imagery.” Abacus math uses the left-hemisphere to understand the logic of arithmetic and then allows a child to use the right-hemisphere to project this image of the abacus to do the math. We named this rare case “abacus-based acalculia.” Together with previous neuroimaging studies, the present result suggests an important role for the PMd and parietal cortex in the superior arithmetic ability of abacus users. "This is the first case report on the impairment of the mental abacus by a brain lesion and on recovery-related brain activity. The power of Anzan, mental math by imagining the abacus.Ī study published in 2012 marks the incredible journey of an abacus student who suffered a stroke and her incredible recovery with abacus math."Previous studies in the field of abacus-based mental calculation (AMC) training have shown that this training has the potential to enhance a wide variety of cognitive abilities" With our program, your child will want to practice so that it's not just dry numbers but a fun atmosphere where he can battle with other peers, earn rewards, badges, and, best of all, achieve results. Let me point out, the underlying secret behind an authentic abacus program is.do it because there is no doubt it works. We have incorporated the Soroban Abacus Mental Math training into a fun program that will motivate your child to learn. The great challenge in our Western Hemisphere, which Abacus Mental Math has been able to solve, is to provide a proven, complete curriculum (Pre-Soroban levels, Grades 10-1, and the following Dan-levels) to bring your child the powerful results the Eastern Hemisphere has achieved in arithmetic through the Soroban. Our proven curriculum is designed to help your child succeed in math and achieve the results millions of children worldwide have attained. The question is, where can I find a proven course that will train my child in all three aspects of Soroban training in a way that will engage my child enough to help him gain the skill and access a curriculum that is proven to show results? That is where Abacus Mental Math comes in. To achieve results, you need a proven spiral curriculum and qualified instructors. It would be a misfortune not to give a child the opportunity to avail himself of the incredible math skills he was born with by not giving him Abacus Mental Math training. Anzan can be likened to a virtual reality game, only this game creates synapses in the brain and promotes a healthy, bilateral brain. Once the eyes are exposed long enough, through use, to the Soroban, you no longer need the soroban or a calculator to do the math.Ĭhildren that use the abacus to learn math can create a virtual image (anzan) of the abacus to perform mental calculations. Originating in Japan and now used worldwide, the Soroban abacus is the most effective and most powerful tool for teaching children math, more so, mental math. A most powerful tool tested against time & science. Since OCH 3 is a more activating substituent than CH 3 (i.e. Here is a useful (but not comprehensive) ranking of activating / deactivating groups: (that is, the more activating substituent “wins”) Rule #1: When two or more substituents are present on an aromatic ring, the directing group will be the most activating substituent. The tricky part is that they each direct to different carbons. Here there are two o-, p- directors: –OCH 3 and –CH 3. Let’s look at a slightly more ambiguous example: p-methylanisole. When Two Or More Substituents Are Present, The Directing Group W ill Be The Most A ctivating Substituent. This gives us the product 2-chloro-1- methoxy-4-nitrobenzene, which indeed is the major product. The –NO 2 is a meta- director, and the positions meta- to the NO 2 happen to also be the positions ortho- to the OCH 3.Īs it turns out, both substituents direct to the same position (C–2).The –OCH 3 is an ortho-, para- director, but since the para- position is already substituted (with NO 2), only the ortho- positions are available.The first thing to do is to analyze each substituent individually. Where does the electrophile react? What’s the directing group, OCH 3 or NO 2 ? Say we try to perform an electrophilic aromatic substitution reaction. Let’s start with 1- methoxy-4-nitrobenzene, which also goes by the name, p-nitroanisole. Here’s a thorny question: What happens when we perform an electrophilic aromatic substitution reaction when there are two substituents on benzene?Īnd say that one of them is an ortho-, para- director and one is a meta- director, and they “direct” electrophiles to different carbons on the ring? Electrophilic Aromatic Substitution With Two Directing Groups: Which Group “Wins” ? (Advanced) References and Further Readingġ.Summary: Electrophilic Aromatic Substitution on Disubstituted Benzenes.Nothing Says “Steric Effects” Quite Like A t-Butyl Group.If Attack At Two Or More Positions Is Possible, Pick The Least Sterically Hindered One.When Two Or More Substituents Are Present, The Directing Group Will Be The Most Activating Substituent.Electrophilic Aromatic Substitution With Two Directing Groups: Which Group “Wins” ?.Having gone through the mechanism of electrophilic aromatic substitution, explored activating and deactivating substituents, and seen the importance of directing groups, let’s now take the opportunity to use these concepts to answer some slightly thornier questions. Videos would keep playing, but there was no response to scrolling or other touch inputs, including that x-out to close the notification. Technically, it’s okay, but I recently found when trying to bookmark a course, the pop-up notification asking if I wanted to create a collection would freeze any other inputs. Ideally it would scaffold topics within a learning objective so you don’t have to piece together courses in order to achieve your learning objective You can create a collection, which is kind of the same idea, but because the content is developed separately, you may experience some overlap between courses. Sometimes, though, it would be nice to go deeper on a topic. This can be good or bad, sometimes a short course on a timely topic is what I need. Content is good, but less robust than other learning platforms lke Coursera. Have used for several years, on and off, usually through a work subscription. If there is any additional feedback you'd like to provide, please email us at. We'll pass your comments upward to our team here. We appreciate you taking the time to review the LinkedIn Learning app. Having a format where student can practice and learn-by-doing (a la Codecademy, even lightbot) would be ideal, but I realized this is a lot of work and MONEY that probably won’t be invested. I’d much rather get a copy of the PowerPoints the instructors use (which, oddly, seems to be the only thing omitted from giant exercise files) or cheat sheets to help me in the real world. Many don’t even have instructions enclosed. Additionally, the files I’ve seen are more samples than actual exercises to go thru. It’s a swivel chair nightmare and there is no time built in or guides that even tell you when to open the exercises. So in addition to taking forever to download, I found the exercise files I pretty useless. Lecture exercises can be files up to 2gb -zipped. If you want to learn a technical skill this app is extremely difficult to use. I don’t see ANYTHING with this app that makes it better value than lecture based competitors like udemy, courses, etc. I have a free membership thru my work enterprise, which, honestly, is the only reason I use it. If you’re looking for a lecture, it’s decent.
Eres un verdadero caballo! – You’re a true horse!Įres un verdadero caballero! – You’re a true gentleman!Įstoy muy emocionada! – I am very excited.Este zumo es sin preservativos? – Is this juice without condoms?Įste zumo es sin aditivos? – Is this juice without preservatives?.Estoy muy embarazada – I am very pregnant.Įstoy muy avergonzada. Every language is full of idioms, which are specific words, or whole sentences, that are commonly spoken to mean something beyond their original dictionary definition. amuse - amusing - amusingly - antic - barrel of laughs - belly laugh - blooper - bundle of laughs - cartoon - clever - comic - comic relief - comical - crack a joke - gas - good for a laugh - good laugh - hilarious - hoot - humorless - humorous - hysterical - joke - laugh - merry - outrageous - raise a smile - rapier wit - ridiculous - riot - ro.Mis hombres están cansados – My men are tired.– I would like a salad with the male sexual organ. Anoche comí pecado – Last night I ate sin.Īnoche comí pe scado – Last night I ate fish.Make sure you don’t end up in one of these situations and start learning Spanish now □ Here we have collated the 10 funniest ones we could think of but please hesitate to let us know new ones if you can think of them. Example with Translation: 'ramos cuatro gatos en la fiesta, no te perdiste nada. Figurative Meaning: nobody, hardly anyone. 18 Funniest Spanish Idioms and Expressions 1. Next time you visit a Spanish speaking country, learn a few of the funny things to say in Spanish below. In this post, you’ll learn 43 unique Spanish words and how to use them. Knowing these weird Spanish words won’t just help you understand native speakers but also give you tons of new ways to express ideas. Every learner of a Spanish has probably experienced it before: thinking you said something perfectly but when you looked at the red faces of those around you, you realized that you had made another embarrassing mistake… There are many funny Spanish idioms and expressions, which when used in conversation, will make you sound even more fluent in Spanish. Some words may mean something in English literally, but they mean something completely different in Spanish. Roofing authorities like Hays Plumbing & Heating Inc's are priceless for Las Vegas individuals. The maintenance of this business is guaranteed to be the greatest quality results offered. Be sure to browse their webpage to figure out the work that the roofers from Hays Plumbing & Heating Inc of Las Vegas present. Buildings throughout Las Vegas have profited considerably from roofing jobs by Hays Plumbing & Heating Inc. 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