Cyclic Gray Code A finite Gray code sequence is called cyclic if the transition between the last word of the sequence and the first is a single bit exchange that is the first and last strings differ by a single binary digit. Rather, Gray code is produced by applying the exclusive-or operation to consecutive bits of the equivalent binary number (Table. Where the binary counting system, like the decimal counting system, places the value of a bit or number on the digit’s position, Gray code does not. Gray code is a binary counting system in which consecutive numbers differ by a single bit. Gray Code Tightly coupled with the notion of binary counting is that of Gray Code. A layered Q 3 graph with M 3 outlined in the centerģ. Definition 6 (Word or String) The terms word and string are used interchangeably to refer to a binary number consisting of a sequence of zeros and ones.įigure 2. Definition 5 (Middle Level Graph) The middle layer graph, denoted, is a subgraph of containing the vertices in levels and (Fig. The level of the hypercube refers to the set of vertices of which contain I ones in their vertex string (Fig. Definition 4 (Vertex Levels of a Hypercube) When mapped to a coordinate axis, each vertex of a hypercube,, can be assigned a binary string of length n. Definition 3 (Hamiltonian Cycle) In a graph, a cycle c of, which contains every vertex of once, is said to be a Hamiltonian cycle, and for this reason, is called a Hamiltonian graph. Hypercubes of the first, second and third dimensionĭefinition 2 (Hamiltonian Path) In a graph a path that contains every vertex of once is referred to as a Hamiltonian Path. These graphs are denoted by, where n is the dimension (Fig. For the purpose of this paper it should be noted that all hypercubes refer to binary n-dimensional graphs. Definitions and Notations Definition 1 (Hypercube) A hypercube is the graphical representation of the edges and vertices in a single volumetric unit in any dimension n. Finally, this paper will look into how queue Gray codes can be used to search for paths and cycles within middle level graphs and the results of queue Gray code and antipodal tests on known Hamiltonian paths within various middle level graphs. This paper takes a look at various properties of the hypercube and the middle level graph as well as the use of Gray codes to develop some of these properties. As of 2006, with the aid of technology, and were the largest graphs of this nature to be proved to contain Hamiltonian cycles. There are a few strategies which can be used to disprove the existence of such cycles, but the middle level graph, as little effort will show, fails on these accounts. The difficulty in solving the problem is undoubtedly due in part to the unclear nature of Hamiltonian cycles in general, for there is no known method to prove the existence of a Hamiltonian cycle in a graph. The conjecture states that for every odd n-dimensional hypercube for, there exists a Hamiltonian cycle in the graph of the middle layers of the hypercube. First proposed in the 1980’s by Ivan Havel, the Middle Level Conjecture, under the name “The Revolving Door Conjecture” remains an open problem in mathematics unanimously thought to be true. The question of whether particular subgraphs of the hypercube are Hamiltonian is less clear. It is well known that these graphs are Hamiltonian. Introduction A hypercube, sometimes referred to as a n-cube, is the graphical representation of the edges and vertices in a single volumetric unit in any dimension n. Wang, L., Wang, X., Fu, J., Zhen, L.: A novel probability binary particle swarm optimization algorithm and its application. (eds.) Ad-Hoc, Mobile, and Wireless Networks. Liu, K., Abu-Ghazaleh, N.: Virtual coordinates with backtracking for void traversal in geographic routing. Kratica, J., Kovačević-Vujčić, V., Čangalović, M.: Computing the metric dimension of graphs by genetic algorithms. Khuller, S., Raghavachari, B., Rosenfeld, A.: Landmarks in graphs. Johnson, D.S.: The NP-completeness column: an ongoing guide. In: Information, Decision and Control, IDC 2007, pp. Ilaya, O., Bil, C., Evans, M.: A particle swarm optimisation approach to graph permutations. Harary, F., Melter, R.: On the metric dimension of a graph. 24(12), 2168–2181 (2006)Ĭáceres, J., Hernando, C., Mora, M., Pelayo, I.M., Puertas, M.L., Seara, C., Wood, D.R.: On the metric dimension of Cartesian products of graphs. 102(2), 201–207 (2015)īeerliova, Z., Eberhard, F., Erlebach, T., Hall, A., Hoffmann, M., Mihal’ak, M., Ram, L.S.: Network discovery and verification. Adiwijaya, Salman, A.N.M., Serra, O., Suprijanto, D., Baskoro, E.T.: Some graphs in \(c_f2\) based on \(f\)-coloring.
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(twoDStringArray.getCanonicalName()) // prints (cDoubleArray.getCanonicalName()) //prints doubleĬlass twoDStringArray = String.class (cDouble.getCanonicalName()) // prints doubleĬlass cDoubleArray = Class.forName("[D") (booleanClass.getCanonicalName()) // prints boolean for primitive types, wrapper classes and arrays (concreteClass.getCanonicalName()) // prints because ConcreteClass is not available at compile timeĬoncreteClass = Class.forName("") Eclipse auto completion of method names, hibernate, Struts2 etc. Spring dependency injection, Tomcat web container below method is used most of the times in frameworks like JUnit Get Class using reflectionĬlass concreteClass = ConcreteClass.class ĬoncreteClass = new ConcreteClass(5).getClass() Wrapper classes provide another static variable TYPE to get the class. For primitive types and arrays, we can use static variable class. We can get Class of an object using three methods - through static variable class, using getClass() method of object and (String full圜lassifiedClassName). Let’s look at some of the important refection methods for classes. Package class ConcreteClass extends BaseClass implements BaseInterface In this section, we will look into important methods of Class, for convenience, I am creating some classes and interfaces with inheritance hierarchy. For every type of object, JVM instantiates an immutable instance of that provides methods to examine the runtime properties of the object and create new objects, invoke its method and get/set object fields. is the entry point for all the reflection operations. Primitive types are - boolean, byte, short, int, long, char, float, and double. All the classes, enums, arrays are reference types and inherit from. In java, every object is either a primitive type or reference.
That sounds obvious, sure, but it’s still something to keep in mind, especially once you’ve figured out the type of headset you want and are ready to shop models. Some tethered headsets are more powerful than others. However, just because tethered headsets are typically more powerful than the other types of headsets, that doesn’t make them equal to each other. As we go over them, keep in mind that while each design type has a specific set of pros and cons, that doesn’t mean the various models within that design type embody those qualities equally.įor example, one of the major selling points of tethered VR headsets is their inherent power. Now that we know the different design types of VR headsets, let’s talk about the general pros and cons of each. Merge VR Goggles Headset for Smartphones What are the pros and cons of VR headsets? We’ll get into more specifics later but, for now, you can think of tethered headsets as the most powerful type of VR headsets. The connection cable allows the PC or console to transmit VR signals to the headset, which are then passed on to the user for them to experience. Tethered headsets are VR headsets that have a connection cable linking the headset to a PC or console, depending on the system. Understanding the general design of each will help inform your decision if and when you decide to purchase a VR headset of your own. While there are countless numbers of makers and models of VR headsets, there are only a few different types you need to know about. What are the different types of VR headsets? Some headsets also include built-in stereo sound systems-for a more immersive audio experience-and any combination of tracking sensors, which can translate the wearer’s movements into the virtual world. As the name implies, it’s worn on the head, and it typically features either a pair of stereoscopic displays or specialized lenses that allow the wearer to experience VR. Oculus Go VR Headset What is a VR headset?Īt its most basic, a VR headset is simply a delivery device for VR. The number one factor to consider while shopping, though, are the fabrics that will suit your personal needs. When you're searching for the best leggings with pockets for you, you'll quickly discover that there are many different styles and fits on the market. What to Look For in Leggings With Pockets The leggings on this list come highly rated, meet any budget, and, of course, have pockets deep enough for you to go hands-free. Whether you're looking for a pair of fleece-lined leggings to stay warm in or affordable leggings on Amazon, this list has got you covered. Thus, I set out on a journey to find some-and discovered a ton of different options to satisfy everyone's tastes. The best leggings with pockets just make life easier (if you've ever had to tuck your phone into your sweaty waistband, then you know what I mean). I mean the pockets that blend seamlessly into your leggings and can actually hold all of your essentials. Yes, Fabletics leggings have pockets.No, I'm not talking about the in-your-face hideous side pockets that bulge out of your pants. The back pocket allows you to move freely while keeping your essentials like phone secure. Why do leggings have pockets in the back? Yes, a tailor can add pockets to leggings. Women’s pockets are sewn shut to retain the shape of the garment while it is stored in stores or on a hanger in shops. No, not all leggings have pockets, although most modern leggings do. These products are ideal workout leggings with moisture-wicking properties, breathable material, and soft fabric. She has browsed several online platforms and user feedback to prepare this list of the best workout leggings and yoga pants with pockets. She believes fashion is all about comfort and convenience. The author of this article, Baishali Bhattacharya, is a certified image consultant who loves to keep pace with the latest trends. “This is the perfect legging to pair wiht an oversized colorful bomber jacket that will give you that street look but also be an easy transition to the gym,” opines Libbie Mugrabi, a Fashion Designer. It is available in 14 colors, like black, maroon, purple, and pink. This pair of leggings comes with four pockets – two deep pockets on the sides to conveniently store your phones and two small pockets in the waistband to store your credit cards and keys. The extra-thick waistband tucks in your tummy and makes you look a lot slimmer. It is also equipped with flat-lock stitching that does not dig into your skin or slide down when you squat or jump. The high-rise waistband and non-see-through fabric allows you to enjoy your workouts and yoga comfortably. They are made with soft Spandex material for a comfortable and seamless fit. Wear these yoga pants by IUGA to effortlessly match all your outfits. Libbie Mugrabi, a Fashion Designer recommends, “For a sheek all black look, pair with a matchign black body suit, and oversized blazer, some over the knee pumps, and a black and white little bag! This is perfect for a night out with your girls, but can also be worn to the gym the next day!” The unique high-waisted tummy control waist band contours your curves and streamlines your shape. These pants are equipped with two large pockets on both sides and a hidden inner pocket in the waist to store small items. It also features interlocked seams, which reduce irritation and eliminate chafing for comfort. The lightweight, moisture-wicking fabric is designed to provide comfort along with superior drying and sweat absorption capabilities. Its dense and highly elastic fabric is non-see-through and stretchable. This comfortable pair of yoga pants by Fengbay is made with 23% Spandex and 77% polyester. Pair them a cropped matching sweater, perfect to transition from working out to whatever else your day has in store,” says Libbie Mugrabi, a Fashion Designer. “These legging are perfect for travel or running errands. The brand also offers 100% money-back guarantee, in case you are not satisfied with the product. They also come in various patterns, like solids, jacquard prints, and space dyes. These yoga capri pants come in a wide range of colors, including hot pink, red, white, and indigo blue. The gusseted and flat-lock crotch gives you freedom of movement and are chafe-free. The pants are equipped with two large side pockets, which allow you to store your phone or essentials conveniently. It is made with 13% Spandex and 87% polyester and is moisture-wicking. These high-waisted capri yoga pants by ODODOS are made with a four-way stretch, brushed fabric that allows seamless movement during any pose. Stress relief – Exercise can have beneficial effects on stress and anxiety levels, leaving you feel more calm and relaxed. So, there’s no doubt about the physical benefits of exercise – but what about the benefits of exercise for your brain and emotions?ġ. Mental and emotional benefits of exercise Physical activity can boost blood flow and stimulate the body’s response to oxidative stress, including the production of protective antioxidants. Skin health – Exercise can help protect your skin from damage caused by oxidative stress. Active adults consistently report less fatigue and low energy levels than their sedentary peers.ĥ. But evidence suggests that doing the opposite may boost your energy levels. Energy levels – If you’re feeling lethargic, your first instinct might be to have a lie-down or grab a coffee. If you’re already feeling sniffly, read up on exercising with a cold.Ĥ. Some studies suggest this is due to reduced inflammation, improvements in psychological stress and/or enhanced immuno-surveillance, whilst others cite an increase in white blood cells as a reason. Immune function – Regular exercise is associated with improvements in immune system health, meaning you may be less likely to catch a cold if you keep up your physical activity. If you already have joint issues, find out how to exercise with osteoarthritis.ģ. Weight-bearing activities cause new bone tissue to form and muscles to push and tug against bones, which strengthens both muscles and bones. Strong bones and healthy joints – Exercise can slow age-related losses of muscle mass, bone density and joint lubrication and flexibility. Studies suggest that people who exercise regularly have lowered risk factors for cardiovascular problems, including reduced LDL (bad) and total cholesterol, and increased HDL (good) cholesterol.Ģ. Heart health – Physical activity is associated with a healthy heart. Here are 5 additional physical benefits of regular exercise:ġ. We all know there are benefits to regular exercise - otherwise we might just sit on the couch all the time! Related: Benefits of exercise, Mind-body workouts. Trust me, your body and mind will thank you. Grab your girls, put on some music, and get moving. And the best part? You don't have to do them alone. So there you have it, babes - 5 exercises to improve your body and mind. Whether you’re after the physical or mental health benefits of exercise or both, there's an activity for everyone. Swimming not only works your entire body, but it's also a great way to improve cardiovascular health and relieve stress.ĭancing - Who says exercise has to be boring? Get your groove on with some dance moves and you'll not only burn calories, but you'll also improve your coordination and boost your mood. Swimming - Take a dip in the pool and reap the benefits of this low-impact exercise. Plus, you'll look and feel like a boss babe. It's a great way to improve bone density, increase muscle mass, and boost your confidence. Strength Training - Lifting weights isn't just for bodybuilders, ladies. It's also a great way to burn some calories and get your heart pumping. Running - Lace up those sneakers and hit the pavement, because running is a great way to boost endorphins and clear your mind. Plus, who doesn't love a good downward dog? Yoga - This ancient practice not only improves flexibility and strength, but it also helps to reduce stress and anxiety. We all know how important it is to stay fit, healthy and sexy, but did you know that exercise can also improve your mental health? That's right, babes, it's time to Engage your Mind and Body with these 5 exercises. Hey, what's up babes! It's Team GymDeity, and today we've want to talk about something that's not only good for your body, but also for your mind. Regulations finalized in late 2002 address the eligibility of vacant land for the exclusion. In addition, the taxpayer must not have used the gain exclusion during the immediately preceding two years before the sale. Also, the taxpayer must have occupied and used the home as the taxpayer’s principal residence for at least two years (in the aggregate) of the five years preceding the sale date. §121 exclusion, the taxpayer must have owned the residence for at least two years or more (in the aggregate) during the five years immediately preceding the sale date. In addition, the provision only applies to the taxpayer’s “principal residence.” But, what if the residence is sold with the farm? In that event, how much (if any) of the farmland and outbuildings can be included with the residence under the provision? Also, what if the taxpayer uses a part of the residence for business? How does that impact the exclusion? What if the farm and residence are sold on an installment basis and the buyer defaults and the seller gets the property back? What then? These issues are the focus of today’s blog post. The taxpayer has to meet certain requirements. Of course, the IRS just doesn’t give the exclusion away. It’s one-half of that amount for single filers. The maximum exclusion is $500,000 for taxpayers that are married and file jointly. Section 121 of the Internal Revenue Code provides for the exclusion of gain that is attributable to the sale of the taxpayer’s principal residence. |
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